Algebra Examples

$\frac{x^{5} - 32}{x - 2}$

Step 1

Place the numbers representing the divisor and the dividend into a division-like configuration.

$2$	$1$	$0$	$0$	$0$	$0$	$- 32$

Step 2

The first number in the dividend $(1)$ is put into the first position of the result area (below the horizontal line).

$2$	$1$	$0$	$0$	$0$	$0$	$- 32$

	$1$

Step 3

Multiply the newest entry in the result $(1)$ by the divisor $(2)$ and place the result of $(2)$ under the next term in the dividend $(0)$ .

$2$	$1$	$0$	$0$	$0$	$0$	$- 32$
		$2$
	$1$

Step 4

Add the product of the multiplication and the number from the dividend and put the result in the next position on the result line.

$2$	$1$	$0$	$0$	$0$	$0$	$- 32$
		$2$
	$1$	$2$

Step 5

Multiply the newest entry in the result $(2)$ by the divisor $(2)$ and place the result of $(4)$ under the next term in the dividend $(0)$ .

$2$	$1$	$0$	$0$	$0$	$0$	$- 32$
		$2$	$4$
	$1$	$2$

Step 6

Add the product of the multiplication and the number from the dividend and put the result in the next position on the result line.

$2$	$1$	$0$	$0$	$0$	$0$	$- 32$
		$2$	$4$
	$1$	$2$	$4$

Step 7

Multiply the newest entry in the result $(4)$ by the divisor $(2)$ and place the result of $(8)$ under the next term in the dividend $(0)$ .

$2$	$1$	$0$	$0$	$0$	$0$	$- 32$
		$2$	$4$	$8$
	$1$	$2$	$4$

Step 8

Add the product of the multiplication and the number from the dividend and put the result in the next position on the result line.

$2$	$1$	$0$	$0$	$0$	$0$	$- 32$
		$2$	$4$	$8$
	$1$	$2$	$4$	$8$

Step 9

Multiply the newest entry in the result $(8)$ by the divisor $(2)$ and place the result of $(16)$ under the next term in the dividend $(0)$ .

$2$	$1$	$0$	$0$	$0$	$0$	$- 32$
		$2$	$4$	$8$	$16$
	$1$	$2$	$4$	$8$

Step 10

Add the product of the multiplication and the number from the dividend and put the result in the next position on the result line.

$2$	$1$	$0$	$0$	$0$	$0$	$- 32$
		$2$	$4$	$8$	$16$
	$1$	$2$	$4$	$8$	$16$

Step 11

Multiply the newest entry in the result $(16)$ by the divisor $(2)$ and place the result of $(32)$ under the next term in the dividend $(- 32)$ .

$2$	$1$	$0$	$0$	$0$	$0$	$- 32$
		$2$	$4$	$8$	$16$	$32$
	$1$	$2$	$4$	$8$	$16$

Step 12

Add the product of the multiplication and the number from the dividend and put the result in the next position on the result line.

$2$	$1$	$0$	$0$	$0$	$0$	$- 32$
		$2$	$4$	$8$	$16$	$32$
	$1$	$2$	$4$	$8$	$16$	$0$

Step 13

All numbers except the last become the coefficients of the quotient polynomial. The last value in the result line is the remainder.

$1 x^{4} + 2 x^{3} + 4 x^{2} + 8 x + 16$

Step 14

Simplify the quotient polynomial.

$x^{4} + 2 x^{3} + 4 x^{2} + 8 x + 16$

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