Divide Using Synthetic Division (2x^2-10x-5x^3+x^4)÷(5+x)

$(2 x^{2} - 10 x - 5 x^{3} + x^{4}) \div (5 + x)$

Step 1

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

$- 5$	$1$	$- 5$	$2$	$- 10$	$0$
	\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).

$- 5$	$1$	$- 5$	$2$	$- 10$	$0$
	\xa0				\xa0
	$1$

Step 3

Multiply the newest entry in the result $(1)$ by the divisor $(- 5)$ and place the result of $(- 5)$ under the next term in the dividend $(- 5)$ .

$- 5$	$1$	$- 5$	$2$	$- 10$	$0$
	\xa0	$- 5$			\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.

$- 5$	$1$	$- 5$	$2$	$- 10$	$0$
	\xa0	$- 5$			\xa0
	$1$	$- 10$

Step 5

Multiply the newest entry in the result $(- 10)$ by the divisor $(- 5)$ and place the result of $(50)$ under the next term in the dividend $(2)$ .

$- 5$	$1$	$- 5$	$2$	$- 10$	$0$
	\xa0	$- 5$	$50$		\xa0
	$1$	$- 10$

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.

$- 5$	$1$	$- 5$	$2$	$- 10$	$0$
	\xa0	$- 5$	$50$		\xa0
	$1$	$- 10$	$52$

Step 7

Multiply the newest entry in the result $(52)$ by the divisor $(- 5)$ and place the result of $(- 260)$ under the next term in the dividend $(- 10)$ .

$- 5$	$1$	$- 5$	$2$	$- 10$	$0$
	\xa0	$- 5$	$50$	$- 260$	\xa0
	$1$	$- 10$	$52$

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.

$- 5$	$1$	$- 5$	$2$	$- 10$	$0$
	\xa0	$- 5$	$50$	$- 260$	\xa0
	$1$	$- 10$	$52$	$- 270$

Step 9

Multiply the newest entry in the result $(- 270)$ by the divisor $(- 5)$ and place the result of $(1350)$ under the next term in the dividend $(0)$ .

$- 5$	$1$	$- 5$	$2$	$- 10$	$0$
	\xa0	$- 5$	$50$	$- 260$	$1350$
	$1$	$- 10$	$52$	$- 270$

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.

$- 5$	$1$	$- 5$	$2$	$- 10$	$0$
	\xa0	$- 5$	$50$	$- 260$	$1350$
	$1$	$- 10$	$52$	$- 270$	$1350$

Step 11

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

$1 x^{3} + - 10 x^{2} + (52) x - 270 + \frac{1350}{x + 5}$

Step 12

Simplify the quotient polynomial.

$x^{3} - 10 x^{2} + 52 x - 270 + \frac{1350}{x + 5}$

Divide Using Synthetic Division (2x^2-10x-5x^3+x^4)÷(5+x)

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