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

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

Step 1

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

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

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

Step 3

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 $(- 1)$ .

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

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

Step 5

Multiply the newest entry in the result $(3)$ by the divisor $(2)$ and place the result of $(6)$ under the next term in the dividend $(0)$ .

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

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.

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

Step 7

Multiply the newest entry in the result $(6)$ by the divisor $(2)$ and place the result of $(12)$ under the next term in the dividend $(- 3)$ .

$2$	$2$	$- 1$	$0$	$- 3$	$- 2$	$1$
	\xa0	$4$	$6$	$12$		\xa0
	$2$	$3$	$6$

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.

$2$	$2$	$- 1$	$0$	$- 3$	$- 2$	$1$
	\xa0	$4$	$6$	$12$		\xa0
	$2$	$3$	$6$	$9$

Step 9

Multiply the newest entry in the result $(9)$ by the divisor $(2)$ and place the result of $(18)$ under the next term in the dividend $(- 2)$ .

$2$	$2$	$- 1$	$0$	$- 3$	$- 2$	$1$
	\xa0	$4$	$6$	$12$	$18$	\xa0
	$2$	$3$	$6$	$9$

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.

$2$	$2$	$- 1$	$0$	$- 3$	$- 2$	$1$
	\xa0	$4$	$6$	$12$	$18$	\xa0
	$2$	$3$	$6$	$9$	$16$

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 $(1)$ .

$2$	$2$	$- 1$	$0$	$- 3$	$- 2$	$1$
	\xa0	$4$	$6$	$12$	$18$	$32$
	$2$	$3$	$6$	$9$	$16$

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.

$2$	$2$	$- 1$	$0$	$- 3$	$- 2$	$1$
	\xa0	$4$	$6$	$12$	$18$	$32$
	$2$	$3$	$6$	$9$	$16$	$33$

Step 13

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

$2 x^{4} + 3 x^{3} + 6 x^{2} + 9 x + 16 + \frac{33}{x - 2}$

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