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

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

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

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

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

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

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 $(- 1)$ .

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

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

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

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 $(0)$ .

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

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

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

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 $(3)$ .

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

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

$1$	$2$	$- 1$	$0$	$3$	$- 1$	$5$
	\xa0	$2$	$1$	$1$		\xa0
	$2$	$1$	$1$	$4$

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 $(- 1)$ .

$1$	$2$	$- 1$	$0$	$3$	$- 1$	$5$
	\xa0	$2$	$1$	$1$	$4$	\xa0
	$2$	$1$	$1$	$4$

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

$1$	$2$	$- 1$	$0$	$3$	$- 1$	$5$
	\xa0	$2$	$1$	$1$	$4$	\xa0
	$2$	$1$	$1$	$4$	$3$

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 $(5)$ .

$1$	$2$	$- 1$	$0$	$3$	$- 1$	$5$
	\xa0	$2$	$1$	$1$	$4$	$3$
	$2$	$1$	$1$	$4$	$3$

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

$1$	$2$	$- 1$	$0$	$3$	$- 1$	$5$
	\xa0	$2$	$1$	$1$	$4$	$3$
	$2$	$1$	$1$	$4$	$3$	$8$

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

$2 x^{4} + 1 x^{3} + 1 x^{2} + 4 x + 3 + \frac{8}{x - 1}$

Simplify the quotient polynomial.

$2 x^{4} + x^{3} + x^{2} + 4 x + 3 + \frac{8}{x - 1}$

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