Divide Using Synthetic Division (x^4-256)/(x+4)

$\frac{x^{4} - 256}{x + 4}$

Step 1

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

$- 4$	$1$	$0$	$0$	$0$	$- 256$
	\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).

$- 4$	$1$	$0$	$0$	$0$	$- 256$
	\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 $(0)$ .

$- 4$	$1$	$0$	$0$	$0$	$- 256$
	\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.

$- 4$	$1$	$0$	$0$	$0$	$- 256$
	\xa0	$- 4$			\xa0
	$1$	$- 4$

Step 5

Multiply the newest entry in the result $(- 4)$ by the divisor $(- 4)$ and place the result of $(16)$ under the next term in the dividend $(0)$ .

$- 4$	$1$	$0$	$0$	$0$	$- 256$
	\xa0	$- 4$	$16$		\xa0
	$1$	$- 4$

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.

$- 4$	$1$	$0$	$0$	$0$	$- 256$
	\xa0	$- 4$	$16$		\xa0
	$1$	$- 4$	$16$

Step 7

Multiply the newest entry in the result $(16)$ by the divisor $(- 4)$ and place the result of $(- 64)$ under the next term in the dividend $(0)$ .

$- 4$	$1$	$0$	$0$	$0$	$- 256$
	\xa0	$- 4$	$16$	$- 64$	\xa0
	$1$	$- 4$	$16$

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.

$- 4$	$1$	$0$	$0$	$0$	$- 256$
	\xa0	$- 4$	$16$	$- 64$	\xa0
	$1$	$- 4$	$16$	$- 64$

Step 9

Multiply the newest entry in the result $(- 64)$ by the divisor $(- 4)$ and place the result of $(256)$ under the next term in the dividend $(- 256)$ .

$- 4$	$1$	$0$	$0$	$0$	$- 256$
	\xa0	$- 4$	$16$	$- 64$	$256$
	$1$	$- 4$	$16$	$- 64$

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.

$- 4$	$1$	$0$	$0$	$0$	$- 256$
	\xa0	$- 4$	$16$	$- 64$	$256$
	$1$	$- 4$	$16$	$- 64$	$0$

Step 11

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

$1 x^{3} + - 4 x^{2} + (16) x - 64$

Step 12

Simplify the quotient polynomial.

$x^{3} - 4 x^{2} + 16 x - 64$

Divide Using Synthetic Division (x^4-256)/(x+4)

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