代数示例

$32 x^{11} y^{8} \div 8 x^{6} y^{2}$

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。

$8 x^{6} y^{2}$

+

$0 x^{5}$

+

$0 x^{4}$

+

$0 x^{3}$

+

$0 x^{2}$

+

$0 x$

+

$0$

$32 x^{11} y^{8}$

+

$0 x^{10}$

+

$0 x^{9}$

+

$0 x^{8}$

+

$0 x^{7}$

+

$0 x^{6}$

+

$0 x^{5}$

+

$0 x^{4}$

+

$0 x^{3}$

+

$0 x^{2}$

+

$0 x$

+

$0$

解题步骤 2

将被除数中的最高阶项 $32 x^{11} y^{8}$ 除以除数中的最高阶项 $8 x^{6} y^{2}$ 。

$4 x^{5} y^{6}$

$8 x^{6} y^{2}$

+

$0 x^{5}$

+

$0 x^{4}$

+

$0 x^{3}$

+

$0 x^{2}$

+

$0 x$

+

$0$

$32 x^{11} y^{8}$

+

$0 x^{10}$

+

$0 x^{9}$

+

$0 x^{8}$

+

$0 x^{7}$

+

$0 x^{6}$

+

$0 x^{5}$

+

$0 x^{4}$

+

$0 x^{3}$

+

$0 x^{2}$

+

$0 x$

+

$0$

解题步骤 3

将新的商式项乘以除数。

$4 x^{5} y^{6}$

$8 x^{6} y^{2}$

+

$0 x^{5}$

+

$0 x^{4}$

+

$0 x^{3}$

+

$0 x^{2}$

+

$0 x$

+

$0$

$32 x^{11} y^{8}$

+

$0 x^{10}$

+

$0 x^{9}$

+

$0 x^{8}$

+

$0 x^{7}$

+

$0 x^{6}$

+

$0 x^{5}$

+

$0 x^{4}$

+

$0 x^{3}$

+

$0 x^{2}$

+

$0 x$

+

$0$

+

$32 x^{11} y^{8}$

+

$0$

+

$0$

+

$0$

+

$0$

+

$0$

+

$0$

解题步骤 4

因为要从被除数中减去该表达式，所以应改变 $32 x^{11} y^{8} + 0 + 0 + 0 + 0 + 0 + 0$ 中的所有符号

$4 x^{5} y^{6}$

$8 x^{6} y^{2}$

+

$0 x^{5}$

+

$0 x^{4}$

+

$0 x^{3}$

+

$0 x^{2}$

+

$0 x$

+

$0$

$32 x^{11} y^{8}$

+

$0 x^{10}$

+

$0 x^{9}$

+

$0 x^{8}$

+

$0 x^{7}$

+

$0 x^{6}$

+

$0 x^{5}$

+

$0 x^{4}$

+

$0 x^{3}$

+

$0 x^{2}$

+

$0 x$

+

$0$

-

$32 x^{11} y^{8}$

-

$0$

-

$0$

-

$0$

-

$0$

-

$0$

-

$0$

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。

$4 x^{5} y^{6}$

$8 x^{6} y^{2}$

+

$0 x^{5}$

+

$0 x^{4}$

+

$0 x^{3}$

+

$0 x^{2}$

+

$0 x$

+

$0$

$32 x^{11} y^{8}$

+

$0 x^{10}$

+

$0 x^{9}$

+

$0 x^{8}$

+

$0 x^{7}$

+

$0 x^{6}$

+

$0 x^{5}$

+

$0 x^{4}$

+

$0 x^{3}$

+

$0 x^{2}$

+

$0 x$

+

$0$

-

$32 x^{11} y^{8}$

-

$0$

-

$0$

-

$0$

-

$0$

-

$0$

-

$0$

$0$

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。

$4 x^{5} y^{6}$

$8 x^{6} y^{2}$

+

$0 x^{5}$

+

$0 x^{4}$

+

$0 x^{3}$

+

$0 x^{2}$

+

$0 x$

+

$0$

$32 x^{11} y^{8}$

+

$0 x^{10}$

+

$0 x^{9}$

+

$0 x^{8}$

+

$0 x^{7}$

+

$0 x^{6}$

+

$0 x^{5}$

+

$0 x^{4}$

+

$0 x^{3}$

+

$0 x^{2}$

+

$0 x$

+

$0$

-

$32 x^{11} y^{8}$

-

$0$

-

$0$

-

$0$

-

$0$

-

$0$

-

$0$

$0$

+

$0 x^{4}$

+

$0 x^{3}$

+

$0 x^{2}$

+

$0 x$

+

$0$

解题步骤 7

因为余数为 $0$ ，所以最终答案是商。

$4 x^{5} y^{6}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$