Divide Using Synthetic Division (2x^2-12x-6x^3+x^4)÷(6+x)

$(2 x^{2} - 12 x - 6 x^{3} + x^{4}) \div (6 + x)$

Step 1

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

$- 6$	$1$	$- 6$	$2$	$- 12$	$0$
	\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).

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

Step 3

Multiply the newest entry in the result $(1)$ by the divisor $(- 6)$ and place the result of $(- 6)$ under the next term in the dividend $(- 6)$ .

$- 6$	$1$	$- 6$	$2$	$- 12$	$0$
	\xa0	$- 6$			\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.

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

Step 5

Multiply the newest entry in the result $(- 12)$ by the divisor $(- 6)$ and place the result of $(72)$ under the next term in the dividend $(2)$ .

$- 6$	$1$	$- 6$	$2$	$- 12$	$0$
	\xa0	$- 6$	$72$		\xa0
	$1$	$- 12$

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.

$- 6$	$1$	$- 6$	$2$	$- 12$	$0$
	\xa0	$- 6$	$72$		\xa0
	$1$	$- 12$	$74$

Step 7

Multiply the newest entry in the result $(74)$ by the divisor $(- 6)$ and place the result of $(- 444)$ under the next term in the dividend $(- 12)$ .

$- 6$	$1$	$- 6$	$2$	$- 12$	$0$
	\xa0	$- 6$	$72$	$- 444$	\xa0
	$1$	$- 12$	$74$

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.

$- 6$	$1$	$- 6$	$2$	$- 12$	$0$
	\xa0	$- 6$	$72$	$- 444$	\xa0
	$1$	$- 12$	$74$	$- 456$

Step 9

Multiply the newest entry in the result $(- 456)$ by the divisor $(- 6)$ and place the result of $(2736)$ under the next term in the dividend $(0)$ .

$- 6$	$1$	$- 6$	$2$	$- 12$	$0$
	\xa0	$- 6$	$72$	$- 444$	$2736$
	$1$	$- 12$	$74$	$- 456$

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.

$- 6$	$1$	$- 6$	$2$	$- 12$	$0$
	\xa0	$- 6$	$72$	$- 444$	$2736$
	$1$	$- 12$	$74$	$- 456$	$2736$

Step 11

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

$1 x^{3} + - 12 x^{2} + (74) x - 456 + \frac{2736}{x + 6}$

Step 12

Simplify the quotient polynomial.

$x^{3} - 12 x^{2} + 74 x - 456 + \frac{2736}{x + 6}$

Divide Using Synthetic Division (2x^2-12x-6x^3+x^4)÷(6+x)

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