Divide Using Synthetic Division (x^5+32)/(x+2)

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

Step 1

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

$- 2$	$1$	$0$	$0$	$0$	$0$	$32$
	\xa0					\xa0

Step 2

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

$- 2$	$1$	$0$	$0$	$0$	$0$	$32$
	\xa0					\xa0
	$1$

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 $(0)$ .

$- 2$	$1$	$0$	$0$	$0$	$0$	$32$
	\xa0	$- 2$				\xa0
	$1$

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.

$- 2$	$1$	$0$	$0$	$0$	$0$	$32$
	\xa0	$- 2$				\xa0
	$1$	$- 2$

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 $(0)$ .

$- 2$	$1$	$0$	$0$	$0$	$0$	$32$
	\xa0	$- 2$	$4$			\xa0
	$1$	$- 2$

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.

$- 2$	$1$	$0$	$0$	$0$	$0$	$32$
	\xa0	$- 2$	$4$			\xa0
	$1$	$- 2$	$4$

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 $(0)$ .

$- 2$	$1$	$0$	$0$	$0$	$0$	$32$
	\xa0	$- 2$	$4$	$- 8$		\xa0
	$1$	$- 2$	$4$

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.

$- 2$	$1$	$0$	$0$	$0$	$0$	$32$
	\xa0	$- 2$	$4$	$- 8$		\xa0
	$1$	$- 2$	$4$	$- 8$

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 $(0)$ .

$- 2$	$1$	$0$	$0$	$0$	$0$	$32$
	\xa0	$- 2$	$4$	$- 8$	$16$	\xa0
	$1$	$- 2$	$4$	$- 8$

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.

$- 2$	$1$	$0$	$0$	$0$	$0$	$32$
	\xa0	$- 2$	$4$	$- 8$	$16$	\xa0
	$1$	$- 2$	$4$	$- 8$	$16$

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 $(32)$ .

$- 2$	$1$	$0$	$0$	$0$	$0$	$32$
	\xa0	$- 2$	$4$	$- 8$	$16$	$- 32$
	$1$	$- 2$	$4$	$- 8$	$16$

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.

$- 2$	$1$	$0$	$0$	$0$	$0$	$32$
	\xa0	$- 2$	$4$	$- 8$	$16$	$- 32$
	$1$	$- 2$	$4$	$- 8$	$16$	$0$

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.

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

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