Algebra Examples

Use synthetic division to find the result when

2 x^{3} - 5 x^{2} - x + 6

$2 x^{3} - 5 x^{2} - x + 6$ is divided by

x + 1

$x + 1$

Step 1

Write the problem as a mathematical expression.

Use synthetic division to find the result when

\frac{2 x^{3} - 5 x^{2} - x + 6}{x + 1}

$\frac{2 x^{3} - 5 x^{2} - x + 6}{x + 1}$

Step 2

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

$- 1$ $- 1$	$2$ $2$	$- 5$ $- 5$	$- 1$ $- 1$	$6$ $6$

Step 3

The first number in the dividend

(2)

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

$- 1$ $- 1$	$2$ $2$	$- 5$ $- 5$	$- 1$ $- 1$	$6$ $6$

	$2$ $2$

Step 4

Multiply the newest entry in the result

(2)

$(2)$ by the divisor

(- 1)

$(- 1)$ and place the result of

(- 2)

$(- 2)$ under the next term in the dividend

(- 5)

$(- 5)$ .

$- 1$ $- 1$	$2$ $2$	$- 5$ $- 5$	$- 1$ $- 1$	$6$ $6$
		$- 2$ $- 2$
	$2$ $2$

Step 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.

$- 1$ $- 1$	$2$ $2$	$- 5$ $- 5$	$- 1$ $- 1$	$6$ $6$
		$- 2$ $- 2$
	$2$ $2$	$- 7$ $- 7$

Step 6

Multiply the newest entry in the result

(- 7)

$(- 7)$ by the divisor

(- 1)

$(- 1)$ and place the result of

(7)

$(7)$ under the next term in the dividend

(- 1)

$(- 1)$ .

$- 1$ $- 1$	$2$ $2$	$- 5$ $- 5$	$- 1$ $- 1$	$6$ $6$
		$- 2$ $- 2$	$7$ $7$
	$2$ $2$	$- 7$ $- 7$

Step 7

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

$- 1$ $- 1$	$2$ $2$	$- 5$ $- 5$	$- 1$ $- 1$	$6$ $6$
		$- 2$ $- 2$	$7$ $7$
	$2$ $2$	$- 7$ $- 7$	$6$ $6$

Step 8

Multiply the newest entry in the result

(6)

$(6)$ by the divisor

(- 1)

$(- 1)$ and place the result of

(- 6)

$(- 6)$ under the next term in the dividend

(6)

$(6)$ .

$- 1$ $- 1$	$2$ $2$	$- 5$ $- 5$	$- 1$ $- 1$	$6$ $6$
		$- 2$ $- 2$	$7$ $7$	$- 6$ $- 6$
	$2$ $2$	$- 7$ $- 7$	$6$ $6$

Step 9

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

$- 1$ $- 1$	$2$ $2$	$- 5$ $- 5$	$- 1$ $- 1$	$6$ $6$
		$- 2$ $- 2$	$7$ $7$	$- 6$ $- 6$
	$2$ $2$	$- 7$ $- 7$	$6$ $6$	$0$ $0$

Step 10

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} + - 7 x + 6

$2 x^{2} + - 7 x + 6$

Step 11

Simplify the quotient polynomial.

2 x^{2} - 7 x + 6

$2 x^{2} - 7 x + 6$