Divide Using Synthetic Division (8v^5+32v^4+5v+20)÷(v+4)

$(8 v^{5} + 32 v^{4} + 5 v + 20) \div (v + 4)$

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

$- 4$	$8$	$32$	$0$	$0$	$5$	$20$
	\xa0					\xa0

The first number in the dividend $(8)$ is put into the first position of the result area (below the horizontal line).

$- 4$	$8$	$32$	$0$	$0$	$5$	$20$
	\xa0					\xa0
	$8$

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 $(32)$ .

$- 4$	$8$	$32$	$0$	$0$	$5$	$20$
	\xa0	$- 32$				\xa0
	$8$

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

$- 4$	$8$	$32$	$0$	$0$	$5$	$20$
	\xa0	$- 32$				\xa0
	$8$	$0$

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

$- 4$	$8$	$32$	$0$	$0$	$5$	$20$
	\xa0	$- 32$	$0$			\xa0
	$8$	$0$

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

$- 4$	$8$	$32$	$0$	$0$	$5$	$20$
	\xa0	$- 32$	$0$			\xa0
	$8$	$0$	$0$

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

$- 4$	$8$	$32$	$0$	$0$	$5$	$20$
	\xa0	$- 32$	$0$	$0$		\xa0
	$8$	$0$	$0$

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

$- 4$	$8$	$32$	$0$	$0$	$5$	$20$
	\xa0	$- 32$	$0$	$0$		\xa0
	$8$	$0$	$0$	$0$

Multiply the newest entry in the result $(0)$ by the divisor $(- 4)$ and place the result of $(0)$ under the next term in the dividend $(5)$ .

$- 4$	$8$	$32$	$0$	$0$	$5$	$20$
	\xa0	$- 32$	$0$	$0$	$0$	\xa0
	$8$	$0$	$0$	$0$

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

$- 4$	$8$	$32$	$0$	$0$	$5$	$20$
	\xa0	$- 32$	$0$	$0$	$0$	\xa0
	$8$	$0$	$0$	$0$	$5$

Multiply the newest entry in the result $(5)$ by the divisor $(- 4)$ and place the result of $(- 20)$ under the next term in the dividend $(20)$ .

$- 4$	$8$	$32$	$0$	$0$	$5$	$20$
	\xa0	$- 32$	$0$	$0$	$0$	$- 20$
	$8$	$0$	$0$	$0$	$5$

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

$- 4$	$8$	$32$	$0$	$0$	$5$	$20$
	\xa0	$- 32$	$0$	$0$	$0$	$- 20$
	$8$	$0$	$0$	$0$	$5$	$0$

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

$8 v^{4} + 0 v^{3} + 0 v^{2} + 0 v + 5$

Simplify the quotient polynomial.

$8 v^{4} + 5$

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