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

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

Step 1

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

$- 4$	$1$	$- 4$	$3$	$- 12$	$0$
	\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).

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

Step 3

Multiply the newest entry in the result $(1)$ by the divisor $(- 4)$ and place the result of $(- 4)$ under the next term in the dividend $(- 4)$ .

$- 4$	$1$	$- 4$	$3$	$- 12$	$0$
	\xa0	$- 4$			\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.

$- 4$	$1$	$- 4$	$3$	$- 12$	$0$
	\xa0	$- 4$			\xa0
	$1$	$- 8$

Step 5

Multiply the newest entry in the result $(- 8)$ by the divisor $(- 4)$ and place the result of $(32)$ under the next term in the dividend $(3)$ .

$- 4$	$1$	$- 4$	$3$	$- 12$	$0$
	\xa0	$- 4$	$32$		\xa0
	$1$	$- 8$

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.

$- 4$	$1$	$- 4$	$3$	$- 12$	$0$
	\xa0	$- 4$	$32$		\xa0
	$1$	$- 8$	$35$

Step 7

Multiply the newest entry in the result $(35)$ by the divisor $(- 4)$ and place the result of $(- 140)$ under the next term in the dividend $(- 12)$ .

$- 4$	$1$	$- 4$	$3$	$- 12$	$0$
	\xa0	$- 4$	$32$	$- 140$	\xa0
	$1$	$- 8$	$35$

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.

$- 4$	$1$	$- 4$	$3$	$- 12$	$0$
	\xa0	$- 4$	$32$	$- 140$	\xa0
	$1$	$- 8$	$35$	$- 152$

Step 9

Multiply the newest entry in the result $(- 152)$ by the divisor $(- 4)$ and place the result of $(608)$ under the next term in the dividend $(0)$ .

$- 4$	$1$	$- 4$	$3$	$- 12$	$0$
	\xa0	$- 4$	$32$	$- 140$	$608$
	$1$	$- 8$	$35$	$- 152$

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.

$- 4$	$1$	$- 4$	$3$	$- 12$	$0$
	\xa0	$- 4$	$32$	$- 140$	$608$
	$1$	$- 8$	$35$	$- 152$	$608$

Step 11

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

$1 x^{3} + - 8 x^{2} + (35) x - 152 + \frac{608}{x + 4}$

Step 12

Simplify the quotient polynomial.

$x^{3} - 8 x^{2} + 35 x - 152 + \frac{608}{x + 4}$

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

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