代数示例

$(8 m^{7} - 10 m^{5}) \div 2 m^{3}$

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。

$2 m^{3}$

+

$0 m^{2}$

+

$0 m$

+

$0$

$8 m^{7}$

+

$0 m^{6}$

-

$10 m^{5}$

+

$0 m^{4}$

+

$0 m^{3}$

+

$0 m^{2}$

+

$0 m$

+

$0$

解题步骤 2

将被除数中的最高阶项 $8 m^{7}$ 除以除数中的最高阶项 $2 m^{3}$ 。

$4 m^{4}$

$2 m^{3}$

+

$0 m^{2}$

+

$0 m$

+

$0$

$8 m^{7}$

+

$0 m^{6}$

-

$10 m^{5}$

+

$0 m^{4}$

+

$0 m^{3}$

+

$0 m^{2}$

+

$0 m$

+

$0$

解题步骤 3

将新的商式项乘以除数。

$4 m^{4}$

$2 m^{3}$

+

$0 m^{2}$

+

$0 m$

+

$0$

$8 m^{7}$

+

$0 m^{6}$

-

$10 m^{5}$

+

$0 m^{4}$

+

$0 m^{3}$

+

$0 m^{2}$

+

$0 m$

+

$0$

+

$8 m^{7}$

+

$0$

+

$0$

+

$0$

解题步骤 4

因为要从被除数中减去该表达式，所以应改变 $8 m^{7} + 0 + 0 + 0$ 中的所有符号

$4 m^{4}$

$2 m^{3}$

+

$0 m^{2}$

+

$0 m$

+

$0$

$8 m^{7}$

+

$0 m^{6}$

-

$10 m^{5}$

+

$0 m^{4}$

+

$0 m^{3}$

+

$0 m^{2}$

+

$0 m$

+

$0$

-

$8 m^{7}$

-

$0$

-

$0$

-

$0$

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。

$4 m^{4}$

$2 m^{3}$

+

$0 m^{2}$

+

$0 m$

+

$0$

$8 m^{7}$

+

$0 m^{6}$

-

$10 m^{5}$

+

$0 m^{4}$

+

$0 m^{3}$

+

$0 m^{2}$

+

$0 m$

+

$0$

-

$8 m^{7}$

-

$0$

-

$0$

-

$0$

-

$10 m^{5}$

+

$0$

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。

$4 m^{4}$

$2 m^{3}$

+

$0 m^{2}$

+

$0 m$

+

$0$

$8 m^{7}$

+

$0 m^{6}$

-

$10 m^{5}$

+

$0 m^{4}$

+

$0 m^{3}$

+

$0 m^{2}$

+

$0 m$

+

$0$

-

$8 m^{7}$

-

$0$

-

$0$

-

$0$

-

$10 m^{5}$

+

$0$

+

$0 m^{3}$

+

$0 m^{2}$

+

$0 m$

解题步骤 7

将被除数中的最高阶项 $- 10 m^{5}$ 除以除数中的最高阶项 $2 m^{3}$ 。

$4 m^{4}$

+

$0 m^{3}$

-

$5 m^{2}$

$2 m^{3}$

+

$0 m^{2}$

+

$0 m$

+

$0$

$8 m^{7}$

+

$0 m^{6}$

-

$10 m^{5}$

+

$0 m^{4}$

+

$0 m^{3}$

+

$0 m^{2}$

+

$0 m$

+

$0$

-

$8 m^{7}$

-

$0$

-

$0$

-

$0$

-

$10 m^{5}$

+

$0$

+

$0 m^{3}$

+

$0 m^{2}$

+

$0 m$

解题步骤 8

将新的商式项乘以除数。

$4 m^{4}$

+

$0 m^{3}$

-

$5 m^{2}$

$2 m^{3}$

+

$0 m^{2}$

+

$0 m$

+

$0$

$8 m^{7}$

+

$0 m^{6}$

-

$10 m^{5}$

+

$0 m^{4}$

+

$0 m^{3}$

+

$0 m^{2}$

+

$0 m$

+

$0$

-

$8 m^{7}$

-

$0$

-

$0$

-

$0$

-

$10 m^{5}$

+

$0$

+

$0 m^{3}$

+

$0 m^{2}$

+

$0 m$

-

$10 m^{5}$

+

$0$

+

$0$

+

$0$

解题步骤 9

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

$4 m^{4}$

+

$0 m^{3}$

-

$5 m^{2}$

$2 m^{3}$

+

$0 m^{2}$

+

$0 m$

+

$0$

$8 m^{7}$

+

$0 m^{6}$

-

$10 m^{5}$

+

$0 m^{4}$

+

$0 m^{3}$

+

$0 m^{2}$

+

$0 m$

+

$0$

-

$8 m^{7}$

-

$0$

-

$0$

-

$0$

-

$10 m^{5}$

+

$0$

+

$0 m^{3}$

+

$0 m^{2}$

+

$0 m$

+

$10 m^{5}$

-

$0$

-

$0$

-

$0$

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。

$4 m^{4}$

+

$0 m^{3}$

-

$5 m^{2}$

$2 m^{3}$

+

$0 m^{2}$

+

$0 m$

+

$0$

$8 m^{7}$

+

$0 m^{6}$

-

$10 m^{5}$

+

$0 m^{4}$

+

$0 m^{3}$

+

$0 m^{2}$

+

$0 m$

+

$0$

-

$8 m^{7}$

-

$0$

-

$0$

-

$0$

-

$10 m^{5}$

+

$0$

+

$0 m^{3}$

+

$0 m^{2}$

+

$0 m$

+

$10 m^{5}$

-

$0$

-

$0$

-

$0$

$0$

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。

$4 m^{4}$

+

$0 m^{3}$

-

$5 m^{2}$

$2 m^{3}$

+

$0 m^{2}$

+

$0 m$

+

$0$

$8 m^{7}$

+

$0 m^{6}$

-

$10 m^{5}$

+

$0 m^{4}$

+

$0 m^{3}$

+

$0 m^{2}$

+

$0 m$

+

$0$

-

$8 m^{7}$

-

$0$

-

$0$

-

$0$

-

$10 m^{5}$

+

$0$

+

$0 m^{3}$

+

$0 m^{2}$

+

$0 m$

+

$10 m^{5}$

-

$0$

-

$0$

-

$0$

$0$

+

$0 m$

+

$0$

解题步骤 12

因为余数为 $0$ ，所以最终答案是商。

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

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