Divide Using Synthetic Division (x^5-8x^3+24x^2+12x+40)/(x+4)

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

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

$- 4$	$1$	$0$	$- 8$	$24$	$12$	$40$
	\xa0					\xa0

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

$- 4$	$1$	$0$	$- 8$	$24$	$12$	$40$
	\xa0					\xa0
	$1$

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 $(0)$ .

$- 4$	$1$	$0$	$- 8$	$24$	$12$	$40$
	\xa0	$- 4$				\xa0
	$1$

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

$- 4$	$1$	$0$	$- 8$	$24$	$12$	$40$
	\xa0	$- 4$				\xa0
	$1$	$- 4$

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 $(- 8)$ .

$- 4$	$1$	$0$	$- 8$	$24$	$12$	$40$
	\xa0	$- 4$	$16$			\xa0
	$1$	$- 4$

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

$- 4$	$1$	$0$	$- 8$	$24$	$12$	$40$
	\xa0	$- 4$	$16$			\xa0
	$1$	$- 4$	$8$

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 $(24)$ .

$- 4$	$1$	$0$	$- 8$	$24$	$12$	$40$
	\xa0	$- 4$	$16$	$- 32$		\xa0
	$1$	$- 4$	$8$

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

$- 4$	$1$	$0$	$- 8$	$24$	$12$	$40$
	\xa0	$- 4$	$16$	$- 32$		\xa0
	$1$	$- 4$	$8$	$- 8$

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 $(12)$ .

$- 4$	$1$	$0$	$- 8$	$24$	$12$	$40$
	\xa0	$- 4$	$16$	$- 32$	$32$	\xa0
	$1$	$- 4$	$8$	$- 8$

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

$- 4$	$1$	$0$	$- 8$	$24$	$12$	$40$
	\xa0	$- 4$	$16$	$- 32$	$32$	\xa0
	$1$	$- 4$	$8$	$- 8$	$44$

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 $(40)$ .

$- 4$	$1$	$0$	$- 8$	$24$	$12$	$40$
	\xa0	$- 4$	$16$	$- 32$	$32$	$- 176$
	$1$	$- 4$	$8$	$- 8$	$44$

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

$- 4$	$1$	$0$	$- 8$	$24$	$12$	$40$
	\xa0	$- 4$	$16$	$- 32$	$32$	$- 176$
	$1$	$- 4$	$8$	$- 8$	$44$	$- 136$

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

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

Simplify the quotient polynomial.

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

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