Divide Using Synthetic Division (x^6+4x^5-2x^3+7)/(x+1)

$\frac{x^{6} + 4 x^{5} - 2 x^{3} + 7}{x + 1}$

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

$- 1$	$1$	$4$	$0$	$- 2$	$0$	$0$	$7$
	\xa0						\xa0

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

$- 1$	$1$	$4$	$0$	$- 2$	$0$	$0$	$7$
	\xa0						\xa0
	$1$

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

$- 1$	$1$	$4$	$0$	$- 2$	$0$	$0$	$7$
	\xa0	$- 1$					\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.

$- 1$	$1$	$4$	$0$	$- 2$	$0$	$0$	$7$
	\xa0	$- 1$					\xa0
	$1$	$3$

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 $(0)$ .

$- 1$	$1$	$4$	$0$	$- 2$	$0$	$0$	$7$
	\xa0	$- 1$	$- 3$				\xa0
	$1$	$3$

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

$- 1$	$1$	$4$	$0$	$- 2$	$0$	$0$	$7$
	\xa0	$- 1$	$- 3$				\xa0
	$1$	$3$	$- 3$

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 $(- 2)$ .

$- 1$	$1$	$4$	$0$	$- 2$	$0$	$0$	$7$
	\xa0	$- 1$	$- 3$	$3$			\xa0
	$1$	$3$	$- 3$

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

$- 1$	$1$	$4$	$0$	$- 2$	$0$	$0$	$7$
	\xa0	$- 1$	$- 3$	$3$			\xa0
	$1$	$3$	$- 3$	$1$

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

$- 1$	$1$	$4$	$0$	$- 2$	$0$	$0$	$7$
	\xa0	$- 1$	$- 3$	$3$	$- 1$		\xa0
	$1$	$3$	$- 3$	$1$

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

$- 1$	$1$	$4$	$0$	$- 2$	$0$	$0$	$7$
	\xa0	$- 1$	$- 3$	$3$	$- 1$		\xa0
	$1$	$3$	$- 3$	$1$	$- 1$

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

$- 1$	$1$	$4$	$0$	$- 2$	$0$	$0$	$7$
	\xa0	$- 1$	$- 3$	$3$	$- 1$	$1$	\xa0
	$1$	$3$	$- 3$	$1$	$- 1$

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

$- 1$	$1$	$4$	$0$	$- 2$	$0$	$0$	$7$
	\xa0	$- 1$	$- 3$	$3$	$- 1$	$1$	\xa0
	$1$	$3$	$- 3$	$1$	$- 1$	$1$

Multiply the newest entry in the result $(1)$ by the divisor $(- 1)$ and place the result of $(- 1)$ under the next term in the dividend $(7)$ .

$- 1$	$1$	$4$	$0$	$- 2$	$0$	$0$	$7$
	\xa0	$- 1$	$- 3$	$3$	$- 1$	$1$	$- 1$
	$1$	$3$	$- 3$	$1$	$- 1$	$1$

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

$- 1$	$1$	$4$	$0$	$- 2$	$0$	$0$	$7$
	\xa0	$- 1$	$- 3$	$3$	$- 1$	$1$	$- 1$
	$1$	$3$	$- 3$	$1$	$- 1$	$1$	$6$

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

$1 x^{5} + 3 x^{4} - 3 x^{3} + 1 x^{2} + (- 1) x + 1 + \frac{6}{x + 1}$

Simplify the quotient polynomial.

$x^{5} + 3 x^{4} - 3 x^{3} + x^{2} - x + 1 + \frac{6}{x + 1}$

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