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Divide Using Synthetic Division

$(2 x^{3} - x^{2} - 48 x + 15) \div (x - 5)$

Step 1

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

$5$	$2$	$- 1$	$- 48$	$15$

Step 2

The first number in the dividend $(2)$ is put into the first position of the result area (below the horizontal line).

$5$	$2$	$- 1$	$- 48$	$15$

	$2$

Step 3

Multiply the newest entry in the result $(2)$ by the divisor $(5)$ and place the result of $(10)$ under the next term in the dividend $(- 1)$ .

$5$	$2$	$- 1$	$- 48$	$15$
		$10$
	$2$

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.

$5$	$2$	$- 1$	$- 48$	$15$
		$10$
	$2$	$9$

Step 5

Multiply the newest entry in the result $(9)$ by the divisor $(5)$ and place the result of $(45)$ under the next term in the dividend $(- 48)$ .

$5$	$2$	$- 1$	$- 48$	$15$
		$10$	$45$
	$2$	$9$

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.

$5$	$2$	$- 1$	$- 48$	$15$
		$10$	$45$
	$2$	$9$	$- 3$

Step 7

Multiply the newest entry in the result $(- 3)$ by the divisor $(5)$ and place the result of $(- 15)$ under the next term in the dividend $(15)$ .

$5$	$2$	$- 1$	$- 48$	$15$
		$10$	$45$	$- 15$
	$2$	$9$	$- 3$

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.

$5$	$2$	$- 1$	$- 48$	$15$
		$10$	$45$	$- 15$
	$2$	$9$	$- 3$	$0$

Step 9

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

$2 x^{2} + 9 x - 3$

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