代数示例

$\frac{4 x^{19} + x^{2} + 5 x + 9}{x - 1}$

解题步骤 1

要计算余项，请首先除以该多项式。

点击获取更多步骤...

解题步骤 1.1

建立要用于相除的多项式。如果不是对于所有指数都有对应的项，则插入带 $0$ 值的项。

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

解题步骤 1.2

将被除数中的最高阶项 $4 x^{19}$ 除以除数中的最高阶项 $x$ 。

$4 x^{18}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

解题步骤 1.3

将新的商式项乘以除数。

$4 x^{18}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

解题步骤 1.4

因为要从被除数中减去该表达式，所以应改变 $4 x^{19} - 4 x^{18}$ 中的所有符号

$4 x^{18}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

解题步骤 1.5

改变符号后，将相乘所得的多项式和最后的被除数相加，得到新的被除数。

$4 x^{18}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

解题步骤 1.6

从原来的被除数向下提取下一项到当前被除数中。

$4 x^{18}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

解题步骤 1.7

将被除数中的最高阶项 $4 x^{18}$ 除以除数中的最高阶项 $x$ 。

$4 x^{18}$

$4 x^{17}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

解题步骤 1.8

将新的商式项乘以除数。

$4 x^{18}$

$4 x^{17}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

解题步骤 1.9

因为要从被除数中减去该表达式，所以应改变 $4 x^{18} - 4 x^{17}$ 中的所有符号

$4 x^{18}$

$4 x^{17}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

解题步骤 1.10

改变符号后，将相乘所得的多项式和最后的被除数相加，得到新的被除数。

$4 x^{18}$

$4 x^{17}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

解题步骤 1.11

从原来的被除数向下提取下一项到当前被除数中。

$4 x^{18}$

$4 x^{17}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

解题步骤 1.12

将被除数中的最高阶项 $4 x^{17}$ 除以除数中的最高阶项 $x$ 。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

解题步骤 1.13

将新的商式项乘以除数。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

解题步骤 1.14

因为要从被除数中减去该表达式，所以应改变 $4 x^{17} - 4 x^{16}$ 中的所有符号

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

解题步骤 1.15

改变符号后，将相乘所得的多项式和最后的被除数相加，得到新的被除数。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

解题步骤 1.16

从原来的被除数向下提取下一项到当前被除数中。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

解题步骤 1.17

将被除数中的最高阶项 $4 x^{16}$ 除以除数中的最高阶项 $x$ 。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

解题步骤 1.18

将新的商式项乘以除数。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

解题步骤 1.19

因为要从被除数中减去该表达式，所以应改变 $4 x^{16} - 4 x^{15}$ 中的所有符号

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

解题步骤 1.20

改变符号后，将相乘所得的多项式和最后的被除数相加，得到新的被除数。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

解题步骤 1.21

从原来的被除数向下提取下一项到当前被除数中。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

解题步骤 1.22

将被除数中的最高阶项 $4 x^{15}$ 除以除数中的最高阶项 $x$ 。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

解题步骤 1.23

将新的商式项乘以除数。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

解题步骤 1.24

因为要从被除数中减去该表达式，所以应改变 $4 x^{15} - 4 x^{14}$ 中的所有符号

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

解题步骤 1.25

改变符号后，将相乘所得的多项式和最后的被除数相加，得到新的被除数。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

解题步骤 1.26

从原来的被除数向下提取下一项到当前被除数中。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

解题步骤 1.27

将被除数中的最高阶项 $4 x^{14}$ 除以除数中的最高阶项 $x$ 。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

解题步骤 1.28

将新的商式项乘以除数。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

解题步骤 1.29

因为要从被除数中减去该表达式，所以应改变 $4 x^{14} - 4 x^{13}$ 中的所有符号

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

解题步骤 1.30

改变符号后，将相乘所得的多项式和最后的被除数相加，得到新的被除数。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

解题步骤 1.31

从原来的被除数向下提取下一项到当前被除数中。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

解题步骤 1.32

将被除数中的最高阶项 $4 x^{13}$ 除以除数中的最高阶项 $x$ 。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

解题步骤 1.33

将新的商式项乘以除数。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

解题步骤 1.34

因为要从被除数中减去该表达式，所以应改变 $4 x^{13} - 4 x^{12}$ 中的所有符号

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

解题步骤 1.35

改变符号后，将相乘所得的多项式和最后的被除数相加，得到新的被除数。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

解题步骤 1.36

从原来的被除数向下提取下一项到当前被除数中。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

解题步骤 1.37

将被除数中的最高阶项 $4 x^{12}$ 除以除数中的最高阶项 $x$ 。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

解题步骤 1.38

将新的商式项乘以除数。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

$4 x^{12}$

$4 x^{11}$

解题步骤 1.39

因为要从被除数中减去该表达式，所以应改变 $4 x^{12} - 4 x^{11}$ 中的所有符号

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

$4 x^{12}$

$4 x^{11}$

解题步骤 1.40

改变符号后，将相乘所得的多项式和最后的被除数相加，得到新的被除数。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

$4 x^{12}$

$4 x^{11}$

解题步骤 1.41

从原来的被除数向下提取下一项到当前被除数中。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

$4 x^{12}$

$4 x^{11}$

$0 x^{10}$

解题步骤 1.42

将被除数中的最高阶项 $4 x^{11}$ 除以除数中的最高阶项 $x$ 。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$4 x^{10}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

$4 x^{12}$

$4 x^{11}$

$0 x^{10}$

解题步骤 1.43

将新的商式项乘以除数。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$4 x^{10}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

$4 x^{12}$

$4 x^{11}$

$0 x^{10}$

$4 x^{11}$

$4 x^{10}$

解题步骤 1.44

因为要从被除数中减去该表达式，所以应改变 $4 x^{11} - 4 x^{10}$ 中的所有符号

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$4 x^{10}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

$4 x^{12}$

$4 x^{11}$

$0 x^{10}$

$4 x^{11}$

$4 x^{10}$

解题步骤 1.45

改变符号后，将相乘所得的多项式和最后的被除数相加，得到新的被除数。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$4 x^{10}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

$4 x^{12}$

$4 x^{11}$

$0 x^{10}$

$4 x^{11}$

$4 x^{10}$

解题步骤 1.46

从原来的被除数向下提取下一项到当前被除数中。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$4 x^{10}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

$4 x^{12}$

$4 x^{11}$

$0 x^{10}$

$4 x^{11}$

$4 x^{10}$

$0 x^{9}$

解题步骤 1.47

将被除数中的最高阶项 $4 x^{10}$ 除以除数中的最高阶项 $x$ 。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$4 x^{10}$

$4 x^{9}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

$4 x^{12}$

$4 x^{11}$

$0 x^{10}$

$4 x^{11}$

$4 x^{10}$

$0 x^{9}$

解题步骤 1.48

将新的商式项乘以除数。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$4 x^{10}$

$4 x^{9}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

$4 x^{12}$

$4 x^{11}$

$0 x^{10}$

$4 x^{11}$

$4 x^{10}$

$0 x^{9}$

$4 x^{10}$

$4 x^{9}$

解题步骤 1.49

因为要从被除数中减去该表达式，所以应改变 $4 x^{10} - 4 x^{9}$ 中的所有符号

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$4 x^{10}$

$4 x^{9}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

$4 x^{12}$

$4 x^{11}$

$0 x^{10}$

$4 x^{11}$

$4 x^{10}$

$0 x^{9}$

$4 x^{10}$

$4 x^{9}$

解题步骤 1.50

改变符号后，将相乘所得的多项式和最后的被除数相加，得到新的被除数。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$4 x^{10}$

$4 x^{9}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

$4 x^{12}$

$4 x^{11}$

$0 x^{10}$

$4 x^{11}$

$4 x^{10}$

$0 x^{9}$

$4 x^{10}$

$4 x^{9}$

解题步骤 1.51

从原来的被除数向下提取下一项到当前被除数中。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$4 x^{10}$

$4 x^{9}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

$4 x^{12}$

$4 x^{11}$

$0 x^{10}$

$4 x^{11}$

$4 x^{10}$

$0 x^{9}$

$4 x^{10}$

$4 x^{9}$

$0 x^{8}$

解题步骤 1.52

将被除数中的最高阶项 $4 x^{9}$ 除以除数中的最高阶项 $x$ 。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$4 x^{10}$

$4 x^{9}$

$4 x^{8}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

$4 x^{12}$

$4 x^{11}$

$0 x^{10}$

$4 x^{11}$

$4 x^{10}$

$0 x^{9}$

$4 x^{10}$

$4 x^{9}$

$0 x^{8}$

解题步骤 1.53

将新的商式项乘以除数。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$4 x^{10}$

$4 x^{9}$

$4 x^{8}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

$4 x^{12}$

$4 x^{11}$

$0 x^{10}$

$4 x^{11}$

$4 x^{10}$

$0 x^{9}$

$4 x^{10}$

$4 x^{9}$

$0 x^{8}$

$4 x^{9}$

$4 x^{8}$

解题步骤 1.54

因为要从被除数中减去该表达式，所以应改变 $4 x^{9} - 4 x^{8}$ 中的所有符号

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$4 x^{10}$

$4 x^{9}$

$4 x^{8}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

$4 x^{12}$

$4 x^{11}$

$0 x^{10}$

$4 x^{11}$

$4 x^{10}$

$0 x^{9}$

$4 x^{10}$

$4 x^{9}$

$0 x^{8}$

$4 x^{9}$

$4 x^{8}$

解题步骤 1.55

改变符号后，将相乘所得的多项式和最后的被除数相加，得到新的被除数。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$4 x^{10}$

$4 x^{9}$

$4 x^{8}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

$4 x^{12}$

$4 x^{11}$

$0 x^{10}$

$4 x^{11}$

$4 x^{10}$

$0 x^{9}$

$4 x^{10}$

$4 x^{9}$

$0 x^{8}$

$4 x^{9}$

$4 x^{8}$

解题步骤 1.56

从原来的被除数向下提取下一项到当前被除数中。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$4 x^{10}$

$4 x^{9}$

$4 x^{8}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

$4 x^{12}$

$4 x^{11}$

$0 x^{10}$

$4 x^{11}$

$4 x^{10}$

$0 x^{9}$

$4 x^{10}$

$4 x^{9}$

$0 x^{8}$

$4 x^{9}$

$4 x^{8}$

$0 x^{7}$

解题步骤 1.57

将被除数中的最高阶项 $4 x^{8}$ 除以除数中的最高阶项 $x$ 。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$4 x^{10}$

$4 x^{9}$

$4 x^{8}$

$4 x^{7}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

$4 x^{12}$

$4 x^{11}$

$0 x^{10}$

$4 x^{11}$

$4 x^{10}$

$0 x^{9}$

$4 x^{10}$

$4 x^{9}$

$0 x^{8}$

$4 x^{9}$

$4 x^{8}$

$0 x^{7}$

解题步骤 1.58

将新的商式项乘以除数。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$4 x^{10}$

$4 x^{9}$

$4 x^{8}$

$4 x^{7}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

$4 x^{12}$

$4 x^{11}$

$0 x^{10}$

$4 x^{11}$

$4 x^{10}$

$0 x^{9}$

$4 x^{10}$

$4 x^{9}$

$0 x^{8}$

$4 x^{9}$

$4 x^{8}$

$0 x^{7}$

$4 x^{8}$

$4 x^{7}$

解题步骤 1.59

因为要从被除数中减去该表达式，所以应改变 $4 x^{8} - 4 x^{7}$ 中的所有符号

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$4 x^{10}$

$4 x^{9}$

$4 x^{8}$

$4 x^{7}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

$4 x^{12}$

$4 x^{11}$

$0 x^{10}$

$4 x^{11}$

$4 x^{10}$

$0 x^{9}$

$4 x^{10}$

$4 x^{9}$

$0 x^{8}$

$4 x^{9}$

$4 x^{8}$

$0 x^{7}$

$4 x^{8}$

$4 x^{7}$

解题步骤 1.60

改变符号后，将相乘所得的多项式和最后的被除数相加，得到新的被除数。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$4 x^{10}$

$4 x^{9}$

$4 x^{8}$

$4 x^{7}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

$4 x^{12}$

$4 x^{11}$

$0 x^{10}$

$4 x^{11}$

$4 x^{10}$

$0 x^{9}$

$4 x^{10}$

$4 x^{9}$

$0 x^{8}$

$4 x^{9}$

$4 x^{8}$

$0 x^{7}$

$4 x^{8}$

$4 x^{7}$

解题步骤 1.61

从原来的被除数向下提取下一项到当前被除数中。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$4 x^{10}$

$4 x^{9}$

$4 x^{8}$

$4 x^{7}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

$4 x^{12}$

$4 x^{11}$

$0 x^{10}$

$4 x^{11}$

$4 x^{10}$

$0 x^{9}$

$4 x^{10}$

$4 x^{9}$

$0 x^{8}$

$4 x^{9}$

$4 x^{8}$

$0 x^{7}$

$4 x^{8}$

$4 x^{7}$

$0 x^{6}$

解题步骤 1.62

将被除数中的最高阶项 $4 x^{7}$ 除以除数中的最高阶项 $x$ 。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$4 x^{10}$

$4 x^{9}$

$4 x^{8}$

$4 x^{7}$

$4 x^{6}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

$4 x^{12}$

$4 x^{11}$

$0 x^{10}$

$4 x^{11}$

$4 x^{10}$

$0 x^{9}$

$4 x^{10}$

$4 x^{9}$

$0 x^{8}$

$4 x^{9}$

$4 x^{8}$

$0 x^{7}$

$4 x^{8}$

$4 x^{7}$

$0 x^{6}$

解题步骤 1.63

将新的商式项乘以除数。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$4 x^{10}$

$4 x^{9}$

$4 x^{8}$

$4 x^{7}$

$4 x^{6}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

$4 x^{12}$

$4 x^{11}$

$0 x^{10}$

$4 x^{11}$

$4 x^{10}$

$0 x^{9}$

$4 x^{10}$

$4 x^{9}$

$0 x^{8}$

$4 x^{9}$

$4 x^{8}$

$0 x^{7}$

$4 x^{8}$

$4 x^{7}$

$0 x^{6}$

$4 x^{7}$

$4 x^{6}$

解题步骤 1.64

因为要从被除数中减去该表达式，所以应改变 $4 x^{7} - 4 x^{6}$ 中的所有符号

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$4 x^{10}$

$4 x^{9}$

$4 x^{8}$

$4 x^{7}$

$4 x^{6}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

$4 x^{12}$

$4 x^{11}$

$0 x^{10}$

$4 x^{11}$

$4 x^{10}$

$0 x^{9}$

$4 x^{10}$

$4 x^{9}$

$0 x^{8}$

$4 x^{9}$

$4 x^{8}$

$0 x^{7}$

$4 x^{8}$

$4 x^{7}$

$0 x^{6}$

$4 x^{7}$

$4 x^{6}$

解题步骤 1.65

改变符号后，将相乘所得的多项式和最后的被除数相加，得到新的被除数。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$4 x^{10}$

$4 x^{9}$

$4 x^{8}$

$4 x^{7}$

$4 x^{6}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

$4 x^{12}$

$4 x^{11}$

$0 x^{10}$

$4 x^{11}$

$4 x^{10}$

$0 x^{9}$

$4 x^{10}$

$4 x^{9}$

$0 x^{8}$

$4 x^{9}$

$4 x^{8}$

$0 x^{7}$

$4 x^{8}$

$4 x^{7}$

$0 x^{6}$

$4 x^{7}$

$4 x^{6}$

解题步骤 1.66

从原来的被除数向下提取下一项到当前被除数中。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$4 x^{10}$

$4 x^{9}$

$4 x^{8}$

$4 x^{7}$

$4 x^{6}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

$4 x^{12}$

$4 x^{11}$

$0 x^{10}$

$4 x^{11}$

$4 x^{10}$

$0 x^{9}$

$4 x^{10}$

$4 x^{9}$

$0 x^{8}$

$4 x^{9}$

$4 x^{8}$

$0 x^{7}$

$4 x^{8}$

$4 x^{7}$

$0 x^{6}$

$4 x^{7}$

$4 x^{6}$

$0 x^{5}$

解题步骤 1.67

将被除数中的最高阶项 $4 x^{6}$ 除以除数中的最高阶项 $x$ 。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$4 x^{10}$

$4 x^{9}$

$4 x^{8}$

$4 x^{7}$

$4 x^{6}$

$4 x^{5}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

$4 x^{12}$

$4 x^{11}$

$0 x^{10}$

$4 x^{11}$

$4 x^{10}$

$0 x^{9}$

$4 x^{10}$

$4 x^{9}$

$0 x^{8}$

$4 x^{9}$

$4 x^{8}$

$0 x^{7}$

$4 x^{8}$

$4 x^{7}$

$0 x^{6}$

$4 x^{7}$

$4 x^{6}$

$0 x^{5}$

解题步骤 1.68

将新的商式项乘以除数。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$4 x^{10}$

$4 x^{9}$

$4 x^{8}$

$4 x^{7}$

$4 x^{6}$

$4 x^{5}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

$4 x^{12}$

$4 x^{11}$

$0 x^{10}$

$4 x^{11}$

$4 x^{10}$

$0 x^{9}$

$4 x^{10}$

$4 x^{9}$

$0 x^{8}$

$4 x^{9}$

$4 x^{8}$

$0 x^{7}$

$4 x^{8}$

$4 x^{7}$

$0 x^{6}$

$4 x^{7}$

$4 x^{6}$

$0 x^{5}$

$4 x^{6}$

$4 x^{5}$

解题步骤 1.69

因为要从被除数中减去该表达式，所以应改变 $4 x^{6} - 4 x^{5}$ 中的所有符号

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$4 x^{10}$

$4 x^{9}$

$4 x^{8}$

$4 x^{7}$

$4 x^{6}$

$4 x^{5}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

$4 x^{12}$

$4 x^{11}$

$0 x^{10}$

$4 x^{11}$

$4 x^{10}$

$0 x^{9}$

$4 x^{10}$

$4 x^{9}$

$0 x^{8}$

$4 x^{9}$

$4 x^{8}$

$0 x^{7}$

$4 x^{8}$

$4 x^{7}$

$0 x^{6}$

$4 x^{7}$

$4 x^{6}$

$0 x^{5}$

$4 x^{6}$

$4 x^{5}$

解题步骤 1.70

改变符号后，将相乘所得的多项式和最后的被除数相加，得到新的被除数。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$4 x^{10}$

$4 x^{9}$

$4 x^{8}$

$4 x^{7}$

$4 x^{6}$

$4 x^{5}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

$4 x^{12}$

$4 x^{11}$

$0 x^{10}$

$4 x^{11}$

$4 x^{10}$

$0 x^{9}$

$4 x^{10}$

$4 x^{9}$

$0 x^{8}$

$4 x^{9}$

$4 x^{8}$

$0 x^{7}$

$4 x^{8}$

$4 x^{7}$

$0 x^{6}$

$4 x^{7}$

$4 x^{6}$

$0 x^{5}$

$4 x^{6}$

$4 x^{5}$

解题步骤 1.71

从原来的被除数向下提取下一项到当前被除数中。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$4 x^{10}$

$4 x^{9}$

$4 x^{8}$

$4 x^{7}$

$4 x^{6}$

$4 x^{5}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

$4 x^{12}$

$4 x^{11}$

$0 x^{10}$

$4 x^{11}$

$4 x^{10}$

$0 x^{9}$

$4 x^{10}$

$4 x^{9}$

$0 x^{8}$

$4 x^{9}$

$4 x^{8}$

$0 x^{7}$

$4 x^{8}$

$4 x^{7}$

$0 x^{6}$

$4 x^{7}$

$4 x^{6}$

$0 x^{5}$

$4 x^{6}$

$4 x^{5}$

$0 x^{4}$

解题步骤 1.72

将被除数中的最高阶项 $4 x^{5}$ 除以除数中的最高阶项 $x$ 。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$4 x^{10}$

$4 x^{9}$

$4 x^{8}$

$4 x^{7}$

$4 x^{6}$

$4 x^{5}$

$4 x^{4}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

$4 x^{12}$

$4 x^{11}$

$0 x^{10}$

$4 x^{11}$

$4 x^{10}$

$0 x^{9}$

$4 x^{10}$

$4 x^{9}$

$0 x^{8}$

$4 x^{9}$

$4 x^{8}$

$0 x^{7}$

$4 x^{8}$

$4 x^{7}$

$0 x^{6}$

$4 x^{7}$

$4 x^{6}$

$0 x^{5}$

$4 x^{6}$

$4 x^{5}$

$0 x^{4}$

解题步骤 1.73

将新的商式项乘以除数。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$4 x^{10}$

$4 x^{9}$

$4 x^{8}$

$4 x^{7}$

$4 x^{6}$

$4 x^{5}$

$4 x^{4}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

$4 x^{12}$

$4 x^{11}$

$0 x^{10}$

$4 x^{11}$

$4 x^{10}$

$0 x^{9}$

$4 x^{10}$

$4 x^{9}$

$0 x^{8}$

$4 x^{9}$

$4 x^{8}$

$0 x^{7}$

$4 x^{8}$

$4 x^{7}$

$0 x^{6}$

$4 x^{7}$

$4 x^{6}$

$0 x^{5}$

$4 x^{6}$

$4 x^{5}$

$0 x^{4}$

$4 x^{5}$

$4 x^{4}$

解题步骤 1.74

因为要从被除数中减去该表达式，所以应改变 $4 x^{5} - 4 x^{4}$ 中的所有符号

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$4 x^{10}$

$4 x^{9}$

$4 x^{8}$

$4 x^{7}$

$4 x^{6}$

$4 x^{5}$

$4 x^{4}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

$4 x^{12}$

$4 x^{11}$

$0 x^{10}$

$4 x^{11}$

$4 x^{10}$

$0 x^{9}$

$4 x^{10}$

$4 x^{9}$

$0 x^{8}$

$4 x^{9}$

$4 x^{8}$

$0 x^{7}$

$4 x^{8}$

$4 x^{7}$

$0 x^{6}$

$4 x^{7}$

$4 x^{6}$

$0 x^{5}$

$4 x^{6}$

$4 x^{5}$

$0 x^{4}$

$4 x^{5}$

$4 x^{4}$

解题步骤 1.75

改变符号后，将相乘所得的多项式和最后的被除数相加，得到新的被除数。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$4 x^{10}$

$4 x^{9}$

$4 x^{8}$

$4 x^{7}$

$4 x^{6}$

$4 x^{5}$

$4 x^{4}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

$4 x^{12}$

$4 x^{11}$

$0 x^{10}$

$4 x^{11}$

$4 x^{10}$

$0 x^{9}$

$4 x^{10}$

$4 x^{9}$

$0 x^{8}$

$4 x^{9}$

$4 x^{8}$

$0 x^{7}$

$4 x^{8}$

$4 x^{7}$

$0 x^{6}$

$4 x^{7}$

$4 x^{6}$

$0 x^{5}$

$4 x^{6}$

$4 x^{5}$

$0 x^{4}$

$4 x^{5}$

$4 x^{4}$

解题步骤 1.76

从原来的被除数向下提取下一项到当前被除数中。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$4 x^{10}$

$4 x^{9}$

$4 x^{8}$

$4 x^{7}$

$4 x^{6}$

$4 x^{5}$

$4 x^{4}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

$4 x^{12}$

$4 x^{11}$

$0 x^{10}$

$4 x^{11}$

$4 x^{10}$

$0 x^{9}$

$4 x^{10}$

$4 x^{9}$

$0 x^{8}$

$4 x^{9}$

$4 x^{8}$

$0 x^{7}$

$4 x^{8}$

$4 x^{7}$

$0 x^{6}$

$4 x^{7}$

$4 x^{6}$

$0 x^{5}$

$4 x^{6}$

$4 x^{5}$

$0 x^{4}$

$4 x^{5}$

$4 x^{4}$

$0 x^{3}$

解题步骤 1.77

将被除数中的最高阶项 $4 x^{4}$ 除以除数中的最高阶项 $x$ 。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$4 x^{10}$

$4 x^{9}$

$4 x^{8}$

$4 x^{7}$

$4 x^{6}$

$4 x^{5}$

$4 x^{4}$

$4 x^{3}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

$4 x^{12}$

$4 x^{11}$

$0 x^{10}$

$4 x^{11}$

$4 x^{10}$

$0 x^{9}$

$4 x^{10}$

$4 x^{9}$

$0 x^{8}$

$4 x^{9}$

$4 x^{8}$

$0 x^{7}$

$4 x^{8}$

$4 x^{7}$

$0 x^{6}$

$4 x^{7}$

$4 x^{6}$

$0 x^{5}$

$4 x^{6}$

$4 x^{5}$

$0 x^{4}$

$4 x^{5}$

$4 x^{4}$

$0 x^{3}$

解题步骤 1.78

将新的商式项乘以除数。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$4 x^{10}$

$4 x^{9}$

$4 x^{8}$

$4 x^{7}$

$4 x^{6}$

$4 x^{5}$

$4 x^{4}$

$4 x^{3}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

$4 x^{12}$

$4 x^{11}$

$0 x^{10}$

$4 x^{11}$

$4 x^{10}$

$0 x^{9}$

$4 x^{10}$

$4 x^{9}$

$0 x^{8}$

$4 x^{9}$

$4 x^{8}$

$0 x^{7}$

$4 x^{8}$

$4 x^{7}$

$0 x^{6}$

$4 x^{7}$

$4 x^{6}$

$0 x^{5}$

$4 x^{6}$

$4 x^{5}$

$0 x^{4}$

$4 x^{5}$

$4 x^{4}$

$0 x^{3}$

$4 x^{4}$

$4 x^{3}$

解题步骤 1.79

因为要从被除数中减去该表达式，所以应改变 $4 x^{4} - 4 x^{3}$ 中的所有符号

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$4 x^{10}$

$4 x^{9}$

$4 x^{8}$

$4 x^{7}$

$4 x^{6}$

$4 x^{5}$

$4 x^{4}$

$4 x^{3}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

$4 x^{12}$

$4 x^{11}$

$0 x^{10}$

$4 x^{11}$

$4 x^{10}$

$0 x^{9}$

$4 x^{10}$

$4 x^{9}$

$0 x^{8}$

$4 x^{9}$

$4 x^{8}$

$0 x^{7}$

$4 x^{8}$

$4 x^{7}$

$0 x^{6}$

$4 x^{7}$

$4 x^{6}$

$0 x^{5}$

$4 x^{6}$

$4 x^{5}$

$0 x^{4}$

$4 x^{5}$

$4 x^{4}$

$0 x^{3}$

$4 x^{4}$

$4 x^{3}$

解题步骤 1.80

改变符号后，将相乘所得的多项式和最后的被除数相加，得到新的被除数。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$4 x^{10}$

$4 x^{9}$

$4 x^{8}$

$4 x^{7}$

$4 x^{6}$

$4 x^{5}$

$4 x^{4}$

$4 x^{3}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

$4 x^{12}$

$4 x^{11}$

$0 x^{10}$

$4 x^{11}$

$4 x^{10}$

$0 x^{9}$

$4 x^{10}$

$4 x^{9}$

$0 x^{8}$

$4 x^{9}$

$4 x^{8}$

$0 x^{7}$

$4 x^{8}$

$4 x^{7}$

$0 x^{6}$

$4 x^{7}$

$4 x^{6}$

$0 x^{5}$

$4 x^{6}$

$4 x^{5}$

$0 x^{4}$

$4 x^{5}$

$4 x^{4}$

$0 x^{3}$

$4 x^{4}$

$4 x^{3}$

解题步骤 1.81

从原来的被除数向下提取下一项到当前被除数中。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$4 x^{10}$

$4 x^{9}$

$4 x^{8}$

$4 x^{7}$

$4 x^{6}$

$4 x^{5}$

$4 x^{4}$

$4 x^{3}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

$4 x^{12}$

$4 x^{11}$

$0 x^{10}$

$4 x^{11}$

$4 x^{10}$

$0 x^{9}$

$4 x^{10}$

$4 x^{9}$

$0 x^{8}$

$4 x^{9}$

$4 x^{8}$

$0 x^{7}$

$4 x^{8}$

$4 x^{7}$

$0 x^{6}$

$4 x^{7}$

$4 x^{6}$

$0 x^{5}$

$4 x^{6}$

$4 x^{5}$

$0 x^{4}$

$4 x^{5}$

$4 x^{4}$

$0 x^{3}$

$4 x^{4}$

$4 x^{3}$

$x^{2}$

解题步骤 1.82

将被除数中的最高阶项 $4 x^{3}$ 除以除数中的最高阶项 $x$ 。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$4 x^{10}$

$4 x^{9}$

$4 x^{8}$

$4 x^{7}$

$4 x^{6}$

$4 x^{5}$

$4 x^{4}$

$4 x^{3}$

$4 x^{2}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

$4 x^{12}$

$4 x^{11}$

$0 x^{10}$

$4 x^{11}$

$4 x^{10}$

$0 x^{9}$

$4 x^{10}$

$4 x^{9}$

$0 x^{8}$

$4 x^{9}$

$4 x^{8}$

$0 x^{7}$

$4 x^{8}$

$4 x^{7}$

$0 x^{6}$

$4 x^{7}$

$4 x^{6}$

$0 x^{5}$

$4 x^{6}$

$4 x^{5}$

$0 x^{4}$

$4 x^{5}$

$4 x^{4}$

$0 x^{3}$

$4 x^{4}$

$4 x^{3}$

$x^{2}$

解题步骤 1.83

将新的商式项乘以除数。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$4 x^{10}$

$4 x^{9}$

$4 x^{8}$

$4 x^{7}$

$4 x^{6}$

$4 x^{5}$

$4 x^{4}$

$4 x^{3}$

$4 x^{2}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

$4 x^{12}$

$4 x^{11}$

$0 x^{10}$

$4 x^{11}$

$4 x^{10}$

$0 x^{9}$

$4 x^{10}$

$4 x^{9}$

$0 x^{8}$

$4 x^{9}$

$4 x^{8}$

$0 x^{7}$

$4 x^{8}$

$4 x^{7}$

$0 x^{6}$

$4 x^{7}$

$4 x^{6}$

$0 x^{5}$

$4 x^{6}$

$4 x^{5}$

$0 x^{4}$

$4 x^{5}$

$4 x^{4}$

$0 x^{3}$

$4 x^{4}$

$4 x^{3}$

$x^{2}$

$4 x^{3}$

$4 x^{2}$

解题步骤 1.84

因为要从被除数中减去该表达式，所以应改变 $4 x^{3} - 4 x^{2}$ 中的所有符号

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$4 x^{10}$

$4 x^{9}$

$4 x^{8}$

$4 x^{7}$

$4 x^{6}$

$4 x^{5}$

$4 x^{4}$

$4 x^{3}$

$4 x^{2}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

$4 x^{12}$

$4 x^{11}$

$0 x^{10}$

$4 x^{11}$

$4 x^{10}$

$0 x^{9}$

$4 x^{10}$

$4 x^{9}$

$0 x^{8}$

$4 x^{9}$

$4 x^{8}$

$0 x^{7}$

$4 x^{8}$

$4 x^{7}$

$0 x^{6}$

$4 x^{7}$

$4 x^{6}$

$0 x^{5}$

$4 x^{6}$

$4 x^{5}$

$0 x^{4}$

$4 x^{5}$

$4 x^{4}$

$0 x^{3}$

$4 x^{4}$

$4 x^{3}$

$x^{2}$

$4 x^{3}$

$4 x^{2}$

解题步骤 1.85

改变符号后，将相乘所得的多项式和最后的被除数相加，得到新的被除数。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$4 x^{10}$

$4 x^{9}$

$4 x^{8}$

$4 x^{7}$

$4 x^{6}$

$4 x^{5}$

$4 x^{4}$

$4 x^{3}$

$4 x^{2}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

$4 x^{12}$

$4 x^{11}$

$0 x^{10}$

$4 x^{11}$

$4 x^{10}$

$0 x^{9}$

$4 x^{10}$

$4 x^{9}$

$0 x^{8}$

$4 x^{9}$

$4 x^{8}$

$0 x^{7}$

$4 x^{8}$

$4 x^{7}$

$0 x^{6}$

$4 x^{7}$

$4 x^{6}$

$0 x^{5}$

$4 x^{6}$

$4 x^{5}$

$0 x^{4}$

$4 x^{5}$

$4 x^{4}$

$0 x^{3}$

$4 x^{4}$

$4 x^{3}$

$x^{2}$

$4 x^{3}$

$4 x^{2}$

$5 x^{2}$

解题步骤 1.86

从原来的被除数向下提取下一项到当前被除数中。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$4 x^{10}$

$4 x^{9}$

$4 x^{8}$

$4 x^{7}$

$4 x^{6}$

$4 x^{5}$

$4 x^{4}$

$4 x^{3}$

$4 x^{2}$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

$4 x^{12}$

$4 x^{11}$

$0 x^{10}$

$4 x^{11}$

$4 x^{10}$

$0 x^{9}$

$4 x^{10}$

$4 x^{9}$

$0 x^{8}$

$4 x^{9}$

$4 x^{8}$

$0 x^{7}$

$4 x^{8}$

$4 x^{7}$

$0 x^{6}$

$4 x^{7}$

$4 x^{6}$

$0 x^{5}$

$4 x^{6}$

$4 x^{5}$

$0 x^{4}$

$4 x^{5}$

$4 x^{4}$

$0 x^{3}$

$4 x^{4}$

$4 x^{3}$

$x^{2}$

$4 x^{3}$

$4 x^{2}$

$5 x^{2}$

$5 x$

解题步骤 1.87

将被除数中的最高阶项 $5 x^{2}$ 除以除数中的最高阶项 $x$ 。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$4 x^{10}$

$4 x^{9}$

$4 x^{8}$

$4 x^{7}$

$4 x^{6}$

$4 x^{5}$

$4 x^{4}$

$4 x^{3}$

$4 x^{2}$

$5 x$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

$4 x^{12}$

$4 x^{11}$

$0 x^{10}$

$4 x^{11}$

$4 x^{10}$

$0 x^{9}$

$4 x^{10}$

$4 x^{9}$

$0 x^{8}$

$4 x^{9}$

$4 x^{8}$

$0 x^{7}$

$4 x^{8}$

$4 x^{7}$

$0 x^{6}$

$4 x^{7}$

$4 x^{6}$

$0 x^{5}$

$4 x^{6}$

$4 x^{5}$

$0 x^{4}$

$4 x^{5}$

$4 x^{4}$

$0 x^{3}$

$4 x^{4}$

$4 x^{3}$

$x^{2}$

$4 x^{3}$

$4 x^{2}$

$5 x^{2}$

$5 x$

解题步骤 1.88

将新的商式项乘以除数。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$4 x^{10}$

$4 x^{9}$

$4 x^{8}$

$4 x^{7}$

$4 x^{6}$

$4 x^{5}$

$4 x^{4}$

$4 x^{3}$

$4 x^{2}$

$5 x$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

$4 x^{12}$

$4 x^{11}$

$0 x^{10}$

$4 x^{11}$

$4 x^{10}$

$0 x^{9}$

$4 x^{10}$

$4 x^{9}$

$0 x^{8}$

$4 x^{9}$

$4 x^{8}$

$0 x^{7}$

$4 x^{8}$

$4 x^{7}$

$0 x^{6}$

$4 x^{7}$

$4 x^{6}$

$0 x^{5}$

$4 x^{6}$

$4 x^{5}$

$0 x^{4}$

$4 x^{5}$

$4 x^{4}$

$0 x^{3}$

$4 x^{4}$

$4 x^{3}$

$x^{2}$

$4 x^{3}$

$4 x^{2}$

$5 x^{2}$

$5 x$

$5 x^{2}$

$5 x$

解题步骤 1.89

因为要从被除数中减去该表达式，所以应改变 $5 x^{2} - 5 x$ 中的所有符号

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$4 x^{10}$

$4 x^{9}$

$4 x^{8}$

$4 x^{7}$

$4 x^{6}$

$4 x^{5}$

$4 x^{4}$

$4 x^{3}$

$4 x^{2}$

$5 x$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

$4 x^{12}$

$4 x^{11}$

$0 x^{10}$

$4 x^{11}$

$4 x^{10}$

$0 x^{9}$

$4 x^{10}$

$4 x^{9}$

$0 x^{8}$

$4 x^{9}$

$4 x^{8}$

$0 x^{7}$

$4 x^{8}$

$4 x^{7}$

$0 x^{6}$

$4 x^{7}$

$4 x^{6}$

$0 x^{5}$

$4 x^{6}$

$4 x^{5}$

$0 x^{4}$

$4 x^{5}$

$4 x^{4}$

$0 x^{3}$

$4 x^{4}$

$4 x^{3}$

$x^{2}$

$4 x^{3}$

$4 x^{2}$

$5 x^{2}$

$5 x$

$5 x^{2}$

$5 x$

解题步骤 1.90

改变符号后，将相乘所得的多项式和最后的被除数相加，得到新的被除数。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$4 x^{10}$

$4 x^{9}$

$4 x^{8}$

$4 x^{7}$

$4 x^{6}$

$4 x^{5}$

$4 x^{4}$

$4 x^{3}$

$4 x^{2}$

$5 x$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

$4 x^{12}$

$4 x^{11}$

$0 x^{10}$

$4 x^{11}$

$4 x^{10}$

$0 x^{9}$

$4 x^{10}$

$4 x^{9}$

$0 x^{8}$

$4 x^{9}$

$4 x^{8}$

$0 x^{7}$

$4 x^{8}$

$4 x^{7}$

$0 x^{6}$

$4 x^{7}$

$4 x^{6}$

$0 x^{5}$

$4 x^{6}$

$4 x^{5}$

$0 x^{4}$

$4 x^{5}$

$4 x^{4}$

$0 x^{3}$

$4 x^{4}$

$4 x^{3}$

$x^{2}$

$4 x^{3}$

$4 x^{2}$

$5 x^{2}$

$5 x$

$5 x^{2}$

$5 x$

$10 x$

解题步骤 1.91

从原来的被除数向下提取下一项到当前被除数中。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$4 x^{10}$

$4 x^{9}$

$4 x^{8}$

$4 x^{7}$

$4 x^{6}$

$4 x^{5}$

$4 x^{4}$

$4 x^{3}$

$4 x^{2}$

$5 x$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

$4 x^{12}$

$4 x^{11}$

$0 x^{10}$

$4 x^{11}$

$4 x^{10}$

$0 x^{9}$

$4 x^{10}$

$4 x^{9}$

$0 x^{8}$

$4 x^{9}$

$4 x^{8}$

$0 x^{7}$

$4 x^{8}$

$4 x^{7}$

$0 x^{6}$

$4 x^{7}$

$4 x^{6}$

$0 x^{5}$

$4 x^{6}$

$4 x^{5}$

$0 x^{4}$

$4 x^{5}$

$4 x^{4}$

$0 x^{3}$

$4 x^{4}$

$4 x^{3}$

$x^{2}$

$4 x^{3}$

$4 x^{2}$

$5 x^{2}$

$5 x$

$5 x^{2}$

$5 x$

$10 x$

$9$

解题步骤 1.92

将被除数中的最高阶项 $10 x$ 除以除数中的最高阶项 $x$ 。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$4 x^{10}$

$4 x^{9}$

$4 x^{8}$

$4 x^{7}$

$4 x^{6}$

$4 x^{5}$

$4 x^{4}$

$4 x^{3}$

$4 x^{2}$

$5 x$

$10$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

$4 x^{12}$

$4 x^{11}$

$0 x^{10}$

$4 x^{11}$

$4 x^{10}$

$0 x^{9}$

$4 x^{10}$

$4 x^{9}$

$0 x^{8}$

$4 x^{9}$

$4 x^{8}$

$0 x^{7}$

$4 x^{8}$

$4 x^{7}$

$0 x^{6}$

$4 x^{7}$

$4 x^{6}$

$0 x^{5}$

$4 x^{6}$

$4 x^{5}$

$0 x^{4}$

$4 x^{5}$

$4 x^{4}$

$0 x^{3}$

$4 x^{4}$

$4 x^{3}$

$x^{2}$

$4 x^{3}$

$4 x^{2}$

$5 x^{2}$

$5 x$

$5 x^{2}$

$5 x$

$10 x$

$9$

解题步骤 1.93

将新的商式项乘以除数。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$4 x^{10}$

$4 x^{9}$

$4 x^{8}$

$4 x^{7}$

$4 x^{6}$

$4 x^{5}$

$4 x^{4}$

$4 x^{3}$

$4 x^{2}$

$5 x$

$10$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

$4 x^{12}$

$4 x^{11}$

$0 x^{10}$

$4 x^{11}$

$4 x^{10}$

$0 x^{9}$

$4 x^{10}$

$4 x^{9}$

$0 x^{8}$

$4 x^{9}$

$4 x^{8}$

$0 x^{7}$

$4 x^{8}$

$4 x^{7}$

$0 x^{6}$

$4 x^{7}$

$4 x^{6}$

$0 x^{5}$

$4 x^{6}$

$4 x^{5}$

$0 x^{4}$

$4 x^{5}$

$4 x^{4}$

$0 x^{3}$

$4 x^{4}$

$4 x^{3}$

$x^{2}$

$4 x^{3}$

$4 x^{2}$

$5 x^{2}$

$5 x$

$5 x^{2}$

$5 x$

$10 x$

$9$

$10 x$

$10$

解题步骤 1.94

因为要从被除数中减去该表达式，所以应改变 $10 x - 10$ 中的所有符号

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$4 x^{10}$

$4 x^{9}$

$4 x^{8}$

$4 x^{7}$

$4 x^{6}$

$4 x^{5}$

$4 x^{4}$

$4 x^{3}$

$4 x^{2}$

$5 x$

$10$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

$4 x^{12}$

$4 x^{11}$

$0 x^{10}$

$4 x^{11}$

$4 x^{10}$

$0 x^{9}$

$4 x^{10}$

$4 x^{9}$

$0 x^{8}$

$4 x^{9}$

$4 x^{8}$

$0 x^{7}$

$4 x^{8}$

$4 x^{7}$

$0 x^{6}$

$4 x^{7}$

$4 x^{6}$

$0 x^{5}$

$4 x^{6}$

$4 x^{5}$

$0 x^{4}$

$4 x^{5}$

$4 x^{4}$

$0 x^{3}$

$4 x^{4}$

$4 x^{3}$

$x^{2}$

$4 x^{3}$

$4 x^{2}$

$5 x^{2}$

$5 x$

$5 x^{2}$

$5 x$

$10 x$

$9$

$10 x$

$10$

解题步骤 1.95

改变符号后，将相乘所得的多项式和最后的被除数相加，得到新的被除数。

$4 x^{18}$

$4 x^{17}$

$4 x^{16}$

$4 x^{15}$

$4 x^{14}$

$4 x^{13}$

$4 x^{12}$

$4 x^{11}$

$4 x^{10}$

$4 x^{9}$

$4 x^{8}$

$4 x^{7}$

$4 x^{6}$

$4 x^{5}$

$4 x^{4}$

$4 x^{3}$

$4 x^{2}$

$5 x$

$10$

$x$

$1$

$4 x^{19}$

$0 x^{18}$

$0 x^{17}$

$0 x^{16}$

$0 x^{15}$

$0 x^{14}$

$0 x^{13}$

$0 x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$x^{2}$

$5 x$

$9$

$4 x^{19}$

$4 x^{18}$

$0 x^{17}$

$4 x^{18}$

$4 x^{17}$

$0 x^{16}$

$4 x^{17}$

$4 x^{16}$

$0 x^{15}$

$4 x^{16}$

$4 x^{15}$

$0 x^{14}$

$4 x^{15}$

$4 x^{14}$

$0 x^{13}$

$4 x^{14}$

$4 x^{13}$

$0 x^{12}$

$4 x^{13}$

$4 x^{12}$

$0 x^{11}$

$4 x^{12}$

$4 x^{11}$

$0 x^{10}$

$4 x^{11}$

$4 x^{10}$

$0 x^{9}$

$4 x^{10}$

$4 x^{9}$

$0 x^{8}$

$4 x^{9}$

$4 x^{8}$

$0 x^{7}$

$4 x^{8}$

$4 x^{7}$

$0 x^{6}$

$4 x^{7}$

$4 x^{6}$

$0 x^{5}$

$4 x^{6}$

$4 x^{5}$

$0 x^{4}$

$4 x^{5}$

$4 x^{4}$

$0 x^{3}$

$4 x^{4}$

$4 x^{3}$

$x^{2}$

$4 x^{3}$

$4 x^{2}$

$5 x^{2}$

$5 x$

$5 x^{2}$

$5 x$

$10 x$

$9$

$10 x$

$10$

$19$

解题步骤 1.96

最终答案为商加上余数除以除数。

$4 x^{18} + 4 x^{17} + 4 x^{16} + 4 x^{15} + 4 x^{14} + 4 x^{13} + 4 x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{3} + 4 x^{2} + 5 x + 10 + \frac{19}{x - 1}$

解题步骤 2

因为结果表达式的末项为分数，所以该分数的分子为其余数。

$19$

代数 示例

代数示例