Algebra Examples

$(x^{5} - 8 x^{3} + 24 x^{2} + 12 x + 40) \div (x + 4)$

Step 1

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

$- 4$	$1$	$0$	$- 8$	$24$	$12$	$40$

Step 2

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

$- 4$	$1$	$0$	$- 8$	$24$	$12$	$40$

	$1$

Step 3

Multiply the newest entry in the result $(1)$ by the divisor $(- 4)$ and place the result of $(- 4)$ under the next term in the dividend $(0)$ .

$- 4$	$1$	$0$	$- 8$	$24$	$12$	$40$
		$- 4$
	$1$

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.

$- 4$	$1$	$0$	$- 8$	$24$	$12$	$40$
		$- 4$
	$1$	$- 4$

Step 5

Multiply the newest entry in the result $(- 4)$ by the divisor $(- 4)$ and place the result of $(16)$ under the next term in the dividend $(- 8)$ .

$- 4$	$1$	$0$	$- 8$	$24$	$12$	$40$
		$- 4$	$16$
	$1$	$- 4$

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.

$- 4$	$1$	$0$	$- 8$	$24$	$12$	$40$
		$- 4$	$16$
	$1$	$- 4$	$8$

Step 7

Multiply the newest entry in the result $(8)$ by the divisor $(- 4)$ and place the result of $(- 32)$ under the next term in the dividend $(24)$ .

$- 4$	$1$	$0$	$- 8$	$24$	$12$	$40$
		$- 4$	$16$	$- 32$
	$1$	$- 4$	$8$

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.

$- 4$	$1$	$0$	$- 8$	$24$	$12$	$40$
		$- 4$	$16$	$- 32$
	$1$	$- 4$	$8$	$- 8$

Step 9

Multiply the newest entry in the result $(- 8)$ by the divisor $(- 4)$ and place the result of $(32)$ under the next term in the dividend $(12)$ .

$- 4$	$1$	$0$	$- 8$	$24$	$12$	$40$
		$- 4$	$16$	$- 32$	$32$
	$1$	$- 4$	$8$	$- 8$

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.

$- 4$	$1$	$0$	$- 8$	$24$	$12$	$40$
		$- 4$	$16$	$- 32$	$32$
	$1$	$- 4$	$8$	$- 8$	$44$

Step 11

Multiply the newest entry in the result $(44)$ by the divisor $(- 4)$ and place the result of $(- 176)$ under the next term in the dividend $(40)$ .

$- 4$	$1$	$0$	$- 8$	$24$	$12$	$40$
		$- 4$	$16$	$- 32$	$32$	$- 176$
	$1$	$- 4$	$8$	$- 8$	$44$

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.

$- 4$	$1$	$0$	$- 8$	$24$	$12$	$40$
		$- 4$	$16$	$- 32$	$32$	$- 176$
	$1$	$- 4$	$8$	$- 8$	$44$	$- 136$

Step 13

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

$1 x^{4} + - 4 x^{3} + 8 x^{2} + - 8 x + 44 + \frac{- 136}{x + 4}$

Step 14

Simplify the quotient polynomial.

$x^{4} - 4 x^{3} + 8 x^{2} - 8 x + 44 - \frac{136}{x + 4}$

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