Divide Using Synthetic Division (x^5-13x^4-120x+79)/(x+3)

$\frac{x^{5} - 13 x^{4} - 120 x + 79}{x + 3}$

Step 1

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

$- 3$	$1$	$- 13$	$0$	$0$	$- 120$	$79$
	\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).

$- 3$	$1$	$- 13$	$0$	$0$	$- 120$	$79$
	\xa0					\xa0
	$1$

Step 3

Multiply the newest entry in the result $(1)$ by the divisor $(- 3)$ and place the result of $(- 3)$ under the next term in the dividend $(- 13)$ .

$- 3$	$1$	$- 13$	$0$	$0$	$- 120$	$79$
	\xa0	$- 3$				\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.

$- 3$	$1$	$- 13$	$0$	$0$	$- 120$	$79$
	\xa0	$- 3$				\xa0
	$1$	$- 16$

Step 5

Multiply the newest entry in the result $(- 16)$ by the divisor $(- 3)$ and place the result of $(48)$ under the next term in the dividend $(0)$ .

$- 3$	$1$	$- 13$	$0$	$0$	$- 120$	$79$
	\xa0	$- 3$	$48$			\xa0
	$1$	$- 16$

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.

$- 3$	$1$	$- 13$	$0$	$0$	$- 120$	$79$
	\xa0	$- 3$	$48$			\xa0
	$1$	$- 16$	$48$

Step 7

Multiply the newest entry in the result $(48)$ by the divisor $(- 3)$ and place the result of $(- 144)$ under the next term in the dividend $(0)$ .

$- 3$	$1$	$- 13$	$0$	$0$	$- 120$	$79$
	\xa0	$- 3$	$48$	$- 144$		\xa0
	$1$	$- 16$	$48$

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.

$- 3$	$1$	$- 13$	$0$	$0$	$- 120$	$79$
	\xa0	$- 3$	$48$	$- 144$		\xa0
	$1$	$- 16$	$48$	$- 144$

Step 9

Multiply the newest entry in the result $(- 144)$ by the divisor $(- 3)$ and place the result of $(432)$ under the next term in the dividend $(- 120)$ .

$- 3$	$1$	$- 13$	$0$	$0$	$- 120$	$79$
	\xa0	$- 3$	$48$	$- 144$	$432$	\xa0
	$1$	$- 16$	$48$	$- 144$

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.

$- 3$	$1$	$- 13$	$0$	$0$	$- 120$	$79$
	\xa0	$- 3$	$48$	$- 144$	$432$	\xa0
	$1$	$- 16$	$48$	$- 144$	$312$

Step 11

Multiply the newest entry in the result $(312)$ by the divisor $(- 3)$ and place the result of $(- 936)$ under the next term in the dividend $(79)$ .

$- 3$	$1$	$- 13$	$0$	$0$	$- 120$	$79$
	\xa0	$- 3$	$48$	$- 144$	$432$	$- 936$
	$1$	$- 16$	$48$	$- 144$	$312$

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.

$- 3$	$1$	$- 13$	$0$	$0$	$- 120$	$79$
	\xa0	$- 3$	$48$	$- 144$	$432$	$- 936$
	$1$	$- 16$	$48$	$- 144$	$312$	$- 857$

Step 13

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

$1 x^{4} + - 16 x^{3} + 48 x^{2} + - 144 x + 312 + \frac{- 857}{x + 3}$

Step 14

Simplify the quotient polynomial.

$x^{4} - 16 x^{3} + 48 x^{2} - 144 x + 312 - \frac{857}{x + 3}$

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