代数示例

$(10 m^{8} + 4 m^{6} + 10 m^{5}) \div 2 m^{2}$

解题步骤 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。

$2 m^{2}$

$0 m$

$0$

$10 m^{8}$

$0 m^{7}$

$4 m^{6}$

$10 m^{5}$

$0 m^{4}$

$0 m^{3}$

$0 m^{2}$

$0 m$

$0$

解题步骤 2

将被除数中的最高阶项 $10 m^{8}$ 除以除数中的最高阶项 $2 m^{2}$ 。

$5 m^{6}$

$2 m^{2}$

$0 m$

$0$

$10 m^{8}$

$0 m^{7}$

$4 m^{6}$

$10 m^{5}$

$0 m^{4}$

$0 m^{3}$

$0 m^{2}$

$0 m$

$0$

解题步骤 3

将新的商式项乘以除数。

$5 m^{6}$

$2 m^{2}$

$0 m$

$0$

$10 m^{8}$

$0 m^{7}$

$4 m^{6}$

$10 m^{5}$

$0 m^{4}$

$0 m^{3}$

$0 m^{2}$

$0 m$

$0$

$10 m^{8}$

$0$

解题步骤 4

因为要从被除数中减去该表达式，所以应改变 $10 m^{8} + 0 + 0$ 中的所有符号

$5 m^{6}$

$2 m^{2}$

$0 m$

$0$

$10 m^{8}$

$0 m^{7}$

$4 m^{6}$

$10 m^{5}$

$0 m^{4}$

$0 m^{3}$

$0 m^{2}$

$0 m$

$0$

$10 m^{8}$

$0$

解题步骤 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。

$5 m^{6}$

$2 m^{2}$

$0 m$

$0$

$10 m^{8}$

$0 m^{7}$

$4 m^{6}$

$10 m^{5}$

$0 m^{4}$

$0 m^{3}$

$0 m^{2}$

$0 m$

$0$

$10 m^{8}$

$0$

$4 m^{6}$

解题步骤 6

从原来的被除数向下提取下一项到当前被除数中

$5 m^{6}$

$2 m^{2}$

$0 m$

$0$

$10 m^{8}$

$0 m^{7}$

$4 m^{6}$

$10 m^{5}$

$0 m^{4}$

$0 m^{3}$

$0 m^{2}$

$0 m$

$0$

$10 m^{8}$

$0$

$4 m^{6}$

$10 m^{5}$

$0 m^{4}$

解题步骤 7

将被除数中的最高阶项 $4 m^{6}$ 除以除数中的最高阶项 $2 m^{2}$ 。

$5 m^{6}$

$0 m^{5}$

$2 m^{4}$

$2 m^{2}$

$0 m$

$0$

$10 m^{8}$

$0 m^{7}$

$4 m^{6}$

$10 m^{5}$

$0 m^{4}$

$0 m^{3}$

$0 m^{2}$

$0 m$

$0$

$10 m^{8}$

$0$

$4 m^{6}$

$10 m^{5}$

$0 m^{4}$

解题步骤 8

将新的商式项乘以除数。

$5 m^{6}$

$0 m^{5}$

$2 m^{4}$

$2 m^{2}$

$0 m$

$0$

$10 m^{8}$

$0 m^{7}$

$4 m^{6}$

$10 m^{5}$

$0 m^{4}$

$0 m^{3}$

$0 m^{2}$

$0 m$

$0$

$10 m^{8}$

$0$

$4 m^{6}$

$10 m^{5}$

$0 m^{4}$

$4 m^{6}$

$0$

解题步骤 9

因为要从被除数中减去该表达式，所以应改变 $4 m^{6} + 0 + 0$ 中的所有符号

$5 m^{6}$

$0 m^{5}$

$2 m^{4}$

$2 m^{2}$

$0 m$

$0$

$10 m^{8}$

$0 m^{7}$

$4 m^{6}$

$10 m^{5}$

$0 m^{4}$

$0 m^{3}$

$0 m^{2}$

$0 m$

$0$

$10 m^{8}$

$0$

$4 m^{6}$

$10 m^{5}$

$0 m^{4}$

$4 m^{6}$

$0$

解题步骤 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。

$5 m^{6}$

$0 m^{5}$

$2 m^{4}$

$2 m^{2}$

$0 m$

$0$

$10 m^{8}$

$0 m^{7}$

$4 m^{6}$

$10 m^{5}$

$0 m^{4}$

$0 m^{3}$

$0 m^{2}$

$0 m$

$0$

$10 m^{8}$

$0$

$4 m^{6}$

$10 m^{5}$

$0 m^{4}$

$4 m^{6}$

$0$

$10 m^{5}$

$0$

解题步骤 11

从原来的被除数向下提取下一项到当前被除数中

$5 m^{6}$

$0 m^{5}$

$2 m^{4}$

$2 m^{2}$

$0 m$

$0$

$10 m^{8}$

$0 m^{7}$

$4 m^{6}$

$10 m^{5}$

$0 m^{4}$

$0 m^{3}$

$0 m^{2}$

$0 m$

$0$

$10 m^{8}$

$0$

$4 m^{6}$

$10 m^{5}$

$0 m^{4}$

$4 m^{6}$

$0$

$10 m^{5}$

$0$

$0 m^{3}$

$0 m^{2}$

解题步骤 12

将被除数中的最高阶项 $10 m^{5}$ 除以除数中的最高阶项 $2 m^{2}$ 。

$5 m^{6}$

$0 m^{5}$

$2 m^{4}$

$5 m^{3}$

$2 m^{2}$

$0 m$

$0$

$10 m^{8}$

$0 m^{7}$

$4 m^{6}$

$10 m^{5}$

$0 m^{4}$

$0 m^{3}$

$0 m^{2}$

$0 m$

$0$

$10 m^{8}$

$0$

$4 m^{6}$

$10 m^{5}$

$0 m^{4}$

$4 m^{6}$

$0$

$10 m^{5}$

$0$

$0 m^{3}$

$0 m^{2}$

解题步骤 13

将新的商式项乘以除数。

$5 m^{6}$

$0 m^{5}$

$2 m^{4}$

$5 m^{3}$

$2 m^{2}$

$0 m$

$0$

$10 m^{8}$

$0 m^{7}$

$4 m^{6}$

$10 m^{5}$

$0 m^{4}$

$0 m^{3}$

$0 m^{2}$

$0 m$

$0$

$10 m^{8}$

$0$

$4 m^{6}$

$10 m^{5}$

$0 m^{4}$

$4 m^{6}$

$0$

$10 m^{5}$

$0$

$0 m^{3}$

$0 m^{2}$

$10 m^{5}$

$0$

解题步骤 14

因为要从被除数中减去该表达式，所以应改变 $10 m^{5} + 0 + 0$ 中的所有符号

$5 m^{6}$

$0 m^{5}$

$2 m^{4}$

$5 m^{3}$

$2 m^{2}$

$0 m$

$0$

$10 m^{8}$

$0 m^{7}$

$4 m^{6}$

$10 m^{5}$

$0 m^{4}$

$0 m^{3}$

$0 m^{2}$

$0 m$

$0$

$10 m^{8}$

$0$

$4 m^{6}$

$10 m^{5}$

$0 m^{4}$

$4 m^{6}$

$0$

$10 m^{5}$

$0$

$0 m^{3}$

$0 m^{2}$

$10 m^{5}$

$0$

解题步骤 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。

$5 m^{6}$

$0 m^{5}$

$2 m^{4}$

$5 m^{3}$

$2 m^{2}$

$0 m$

$0$

$10 m^{8}$

$0 m^{7}$

$4 m^{6}$

$10 m^{5}$

$0 m^{4}$

$0 m^{3}$

$0 m^{2}$

$0 m$

$0$

$10 m^{8}$

$0$

$4 m^{6}$

$10 m^{5}$

$0 m^{4}$

$4 m^{6}$

$0$

$10 m^{5}$

$0$

$0 m^{3}$

$0 m^{2}$

$10 m^{5}$

$0$

解题步骤 16

从原来的被除数向下提取下一项到当前被除数中。

$5 m^{6}$

$0 m^{5}$

$2 m^{4}$

$5 m^{3}$

$2 m^{2}$

$0 m$

$0$

$10 m^{8}$

$0 m^{7}$

$4 m^{6}$

$10 m^{5}$

$0 m^{4}$

$0 m^{3}$

$0 m^{2}$

$0 m$

$0$

$10 m^{8}$

$0$

$4 m^{6}$

$10 m^{5}$

$0 m^{4}$

$4 m^{6}$

$0$

$10 m^{5}$

$0$

$0 m^{3}$

$0 m^{2}$

$10 m^{5}$

$0$

$0 m^{2}$

$0 m$

$0$

解题步骤 17

因为余数为 $0$ ，所以最终答案是商。

$5 m^{6} + 0 m^{5} + 2 m^{4} + 5 m^{3}$

代数 示例

代数示例