Divide Using Synthetic Division x^4-10x^2-13x-50 is divided by x+5

$x^{4} - 10 x^{2} - 13 x - 50$ is divided by $x + 5$

Write the problem as a mathematical expression.

$\frac{x^{4} - 10 x^{2} - 13 x - 50}{x + 5}$

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

$- 5$	$1$	$0$	$- 10$	$- 13$	$- 50$
	\xa0				\xa0

The first number in the dividend $(1)$ is put into the first position of the result area (below the horizontal line).

$- 5$	$1$	$0$	$- 10$	$- 13$	$- 50$
	\xa0				\xa0
	$1$

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 $(0)$ .

$- 5$	$1$	$0$	$- 10$	$- 13$	$- 50$
	\xa0	$- 5$			\xa0
	$1$

Add the product of the multiplication and the number from the dividend and put the result in the next position on the result line.

$- 5$	$1$	$0$	$- 10$	$- 13$	$- 50$
	\xa0	$- 5$			\xa0
	$1$	$- 5$

Multiply the newest entry in the result $(- 5)$ by the divisor $(- 5)$ and place the result of $(25)$ under the next term in the dividend $(- 10)$ .

$- 5$	$1$	$0$	$- 10$	$- 13$	$- 50$
	\xa0	$- 5$	$25$		\xa0
	$1$	$- 5$

Add the product of the multiplication and the number from the dividend and put the result in the next position on the result line.

$- 5$	$1$	$0$	$- 10$	$- 13$	$- 50$
	\xa0	$- 5$	$25$		\xa0
	$1$	$- 5$	$15$

Multiply the newest entry in the result $(15)$ by the divisor $(- 5)$ and place the result of $(- 75)$ under the next term in the dividend $(- 13)$ .

$- 5$	$1$	$0$	$- 10$	$- 13$	$- 50$
	\xa0	$- 5$	$25$	$- 75$	\xa0
	$1$	$- 5$	$15$

Add the product of the multiplication and the number from the dividend and put the result in the next position on the result line.

$- 5$	$1$	$0$	$- 10$	$- 13$	$- 50$
	\xa0	$- 5$	$25$	$- 75$	\xa0
	$1$	$- 5$	$15$	$- 88$

Multiply the newest entry in the result $(- 88)$ by the divisor $(- 5)$ and place the result of $(440)$ under the next term in the dividend $(- 50)$ .

$- 5$	$1$	$0$	$- 10$	$- 13$	$- 50$
	\xa0	$- 5$	$25$	$- 75$	$440$
	$1$	$- 5$	$15$	$- 88$

Add the product of the multiplication and the number from the dividend and put the result in the next position on the result line.

$- 5$	$1$	$0$	$- 10$	$- 13$	$- 50$
	\xa0	$- 5$	$25$	$- 75$	$440$
	$1$	$- 5$	$15$	$- 88$	$390$

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

$1 x^{3} + - 5 x^{2} + (15) x - 88 + \frac{390}{x + 5}$

Simplify the quotient polynomial.

$x^{3} - 5 x^{2} + 15 x - 88 + \frac{390}{x + 5}$

Divide Using Synthetic Division x^4-10x^2-13x-50 is divided by x+5

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