Divide Using Synthetic Division (-2x^5-x^3+5x+1)/(x+1)

$\frac{- 2 x^{5} - x^{3} + 5 x + 1}{x + 1}$

Step 1

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

$- 1$	$- 2$	$0$	$- 1$	$0$	$5$	$1$
	\xa0					\xa0

Step 2

The first number in the dividend $(- 2)$ is put into the first position of the result area (below the horizontal line).

$- 1$	$- 2$	$0$	$- 1$	$0$	$5$	$1$
	\xa0					\xa0
	$- 2$

Step 3

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

$- 1$	$- 2$	$0$	$- 1$	$0$	$5$	$1$
	\xa0	$2$				\xa0
	$- 2$

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.

$- 1$	$- 2$	$0$	$- 1$	$0$	$5$	$1$
	\xa0	$2$				\xa0
	$- 2$	$2$

Step 5

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

$- 1$	$- 2$	$0$	$- 1$	$0$	$5$	$1$
	\xa0	$2$	$- 2$			\xa0
	$- 2$	$2$

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.

$- 1$	$- 2$	$0$	$- 1$	$0$	$5$	$1$
	\xa0	$2$	$- 2$			\xa0
	$- 2$	$2$	$- 3$

Step 7

Multiply the newest entry in the result $(- 3)$ by the divisor $(- 1)$ and place the result of $(3)$ under the next term in the dividend $(0)$ .

$- 1$	$- 2$	$0$	$- 1$	$0$	$5$	$1$
	\xa0	$2$	$- 2$	$3$		\xa0
	$- 2$	$2$	$- 3$

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.

$- 1$	$- 2$	$0$	$- 1$	$0$	$5$	$1$
	\xa0	$2$	$- 2$	$3$		\xa0
	$- 2$	$2$	$- 3$	$3$

Step 9

Multiply the newest entry in the result $(3)$ by the divisor $(- 1)$ and place the result of $(- 3)$ under the next term in the dividend $(5)$ .

$- 1$	$- 2$	$0$	$- 1$	$0$	$5$	$1$
	\xa0	$2$	$- 2$	$3$	$- 3$	\xa0
	$- 2$	$2$	$- 3$	$3$

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.

$- 1$	$- 2$	$0$	$- 1$	$0$	$5$	$1$
	\xa0	$2$	$- 2$	$3$	$- 3$	\xa0
	$- 2$	$2$	$- 3$	$3$	$2$

Step 11

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

$- 1$	$- 2$	$0$	$- 1$	$0$	$5$	$1$
	\xa0	$2$	$- 2$	$3$	$- 3$	$- 2$
	$- 2$	$2$	$- 3$	$3$	$2$

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.

$- 1$	$- 2$	$0$	$- 1$	$0$	$5$	$1$
	\xa0	$2$	$- 2$	$3$	$- 3$	$- 2$
	$- 2$	$2$	$- 3$	$3$	$2$	$- 1$

Step 13

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

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

Step 14

Simplify the quotient polynomial.

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

Related Questions