Divide Using Synthetic Division (x^5-10x^2-8)÷(x-2)

$(x^{5} - 10 x^{2} - 8) \div (x - 2)$

Step 1

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

$2$	$1$	$0$	$0$	$- 10$	$0$	$- 8$
	\xa0					\xa0

Step 2

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

$2$	$1$	$0$	$0$	$- 10$	$0$	$- 8$
	\xa0					\xa0
	$1$

Step 3

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

$2$	$1$	$0$	$0$	$- 10$	$0$	$- 8$
	\xa0	$2$				\xa0
	$1$

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.

$2$	$1$	$0$	$0$	$- 10$	$0$	$- 8$
	\xa0	$2$				\xa0
	$1$	$2$

Step 5

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 $(0)$ .

$2$	$1$	$0$	$0$	$- 10$	$0$	$- 8$
	\xa0	$2$	$4$			\xa0
	$1$	$2$

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.

$2$	$1$	$0$	$0$	$- 10$	$0$	$- 8$
	\xa0	$2$	$4$			\xa0
	$1$	$2$	$4$

Step 7

Multiply the newest entry in the result $(4)$ by the divisor $(2)$ and place the result of $(8)$ under the next term in the dividend $(- 10)$ .

$2$	$1$	$0$	$0$	$- 10$	$0$	$- 8$
	\xa0	$2$	$4$	$8$		\xa0
	$1$	$2$	$4$

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.

$2$	$1$	$0$	$0$	$- 10$	$0$	$- 8$
	\xa0	$2$	$4$	$8$		\xa0
	$1$	$2$	$4$	$- 2$

Step 9

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 $(0)$ .

$2$	$1$	$0$	$0$	$- 10$	$0$	$- 8$
	\xa0	$2$	$4$	$8$	$- 4$	\xa0
	$1$	$2$	$4$	$- 2$

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.

$2$	$1$	$0$	$0$	$- 10$	$0$	$- 8$
	\xa0	$2$	$4$	$8$	$- 4$	\xa0
	$1$	$2$	$4$	$- 2$	$- 4$

Step 11

Multiply the newest entry in the result $(- 4)$ by the divisor $(2)$ and place the result of $(- 8)$ under the next term in the dividend $(- 8)$ .

$2$	$1$	$0$	$0$	$- 10$	$0$	$- 8$
	\xa0	$2$	$4$	$8$	$- 4$	$- 8$
	$1$	$2$	$4$	$- 2$	$- 4$

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.

$2$	$1$	$0$	$0$	$- 10$	$0$	$- 8$
	\xa0	$2$	$4$	$8$	$- 4$	$- 8$
	$1$	$2$	$4$	$- 2$	$- 4$	$- 16$

Step 13

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

$1 x^{4} + 2 x^{3} + 4 x^{2} + - 2 x - 4 + \frac{- 16}{x - 2}$

Step 14

Simplify the quotient polynomial.

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

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