Divide Using Synthetic Division (2x^5-2x^3+4x^2-3)÷(x+1)

$(2 x^{5} - 2 x^{3} + 4 x^{2} - 3) \div (x + 1)$

Step 1

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

$- 1$	$2$	$0$	$- 2$	$4$	$0$	$- 3$
	\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).

$- 1$	$2$	$0$	$- 2$	$4$	$0$	$- 3$
	\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 $(0)$ .

$- 1$	$2$	$0$	$- 2$	$4$	$0$	$- 3$
	\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.

$- 1$	$2$	$0$	$- 2$	$4$	$0$	$- 3$
	\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 $(- 2)$ .

$- 1$	$2$	$0$	$- 2$	$4$	$0$	$- 3$
	\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.

$- 1$	$2$	$0$	$- 2$	$4$	$0$	$- 3$
	\xa0	$- 2$	$2$			\xa0
	$2$	$- 2$	$0$

Step 7

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

$- 1$	$2$	$0$	$- 2$	$4$	$0$	$- 3$
	\xa0	$- 2$	$2$	$0$		\xa0
	$2$	$- 2$	$0$

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.

$- 1$	$2$	$0$	$- 2$	$4$	$0$	$- 3$
	\xa0	$- 2$	$2$	$0$		\xa0
	$2$	$- 2$	$0$	$4$

Step 9

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

$- 1$	$2$	$0$	$- 2$	$4$	$0$	$- 3$
	\xa0	$- 2$	$2$	$0$	$- 4$	\xa0
	$2$	$- 2$	$0$	$4$

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.

$- 1$	$2$	$0$	$- 2$	$4$	$0$	$- 3$
	\xa0	$- 2$	$2$	$0$	$- 4$	\xa0
	$2$	$- 2$	$0$	$4$	$- 4$

Step 11

Multiply the newest entry in the result $(- 4)$ by the divisor $(- 1)$ and place the result of $(4)$ under the next term in the dividend $(- 3)$ .

$- 1$	$2$	$0$	$- 2$	$4$	$0$	$- 3$
	\xa0	$- 2$	$2$	$0$	$- 4$	$4$
	$2$	$- 2$	$0$	$4$	$- 4$

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.

$- 1$	$2$	$0$	$- 2$	$4$	$0$	$- 3$
	\xa0	$- 2$	$2$	$0$	$- 4$	$4$
	$2$	$- 2$	$0$	$4$	$- 4$	$1$

Step 13

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

$2 x^{4} + - 2 x^{3} + 0 x^{2} + 4 x - 4 + \frac{1}{x + 1}$

Step 14

Simplify the quotient polynomial.

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

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