Divide Using Synthetic Division (-8x^5+10x^3-100)/(x+2)

$\frac{- 8 x^{5} + 10 x^{3} - 100}{x + 2}$

Step 1

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

$- 2$	$- 8$	$0$	$10$	$0$	$0$	$- 100$
	\xa0					\xa0

Step 2

The first number in the dividend $(- 8)$ is put into the first position of the result area (below the horizontal line).

$- 2$	$- 8$	$0$	$10$	$0$	$0$	$- 100$
	\xa0					\xa0
	$- 8$

Step 3

Multiply the newest entry in the result $(- 8)$ by the divisor $(- 2)$ and place the result of $(16)$ under the next term in the dividend $(0)$ .

$- 2$	$- 8$	$0$	$10$	$0$	$0$	$- 100$
	\xa0	$16$				\xa0
	$- 8$

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.

$- 2$	$- 8$	$0$	$10$	$0$	$0$	$- 100$
	\xa0	$16$				\xa0
	$- 8$	$16$

Step 5

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 $(10)$ .

$- 2$	$- 8$	$0$	$10$	$0$	$0$	$- 100$
	\xa0	$16$	$- 32$			\xa0
	$- 8$	$16$

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.

$- 2$	$- 8$	$0$	$10$	$0$	$0$	$- 100$
	\xa0	$16$	$- 32$			\xa0
	$- 8$	$16$	$- 22$

Step 7

Multiply the newest entry in the result $(- 22)$ by the divisor $(- 2)$ and place the result of $(44)$ under the next term in the dividend $(0)$ .

$- 2$	$- 8$	$0$	$10$	$0$	$0$	$- 100$
	\xa0	$16$	$- 32$	$44$		\xa0
	$- 8$	$16$	$- 22$

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.

$- 2$	$- 8$	$0$	$10$	$0$	$0$	$- 100$
	\xa0	$16$	$- 32$	$44$		\xa0
	$- 8$	$16$	$- 22$	$44$

Step 9

Multiply the newest entry in the result $(44)$ by the divisor $(- 2)$ and place the result of $(- 88)$ under the next term in the dividend $(0)$ .

$- 2$	$- 8$	$0$	$10$	$0$	$0$	$- 100$
	\xa0	$16$	$- 32$	$44$	$- 88$	\xa0
	$- 8$	$16$	$- 22$	$44$

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.

$- 2$	$- 8$	$0$	$10$	$0$	$0$	$- 100$
	\xa0	$16$	$- 32$	$44$	$- 88$	\xa0
	$- 8$	$16$	$- 22$	$44$	$- 88$

Step 11

Multiply the newest entry in the result $(- 88)$ by the divisor $(- 2)$ and place the result of $(176)$ under the next term in the dividend $(- 100)$ .

$- 2$	$- 8$	$0$	$10$	$0$	$0$	$- 100$
	\xa0	$16$	$- 32$	$44$	$- 88$	$176$
	$- 8$	$16$	$- 22$	$44$	$- 88$

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.

$- 2$	$- 8$	$0$	$10$	$0$	$0$	$- 100$
	\xa0	$16$	$- 32$	$44$	$- 88$	$176$
	$- 8$	$16$	$- 22$	$44$	$- 88$	$76$

Step 13

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

$- 8 x^{4} + 16 x^{3} - 22 x^{2} + 44 x - 88 + \frac{76}{x + 2}$

Related Questions