Examples

2 x^{2} + x - 3

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

x - 1

$x - 1$

Step 1

Divide

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

$\frac{2 x^{2} + x - 3}{x - 1}$ using synthetic division and check if the remainder is equal to

0

$0$ . If the remainder is equal to

0

$0$ , it means that

x - 1

$x - 1$ is a factor for

2 x^{2} + x - 3

$2 x^{2} + x - 3$ . If the remainder is not equal to

0

$0$ , it means that

x - 1

$x - 1$ is not a factor for

2 x^{2} + x - 3

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

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Step 1.1

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

$1$ $1$	$2$ $2$	$1$ $1$	$- 3$ $- 3$

Step 1.2

The first number in the dividend

(2)

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

$1$ $1$	$2$ $2$	$1$ $1$	$- 3$ $- 3$

	$2$ $2$

Step 1.3

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

(1)

$(1)$ .

$1$ $1$	$2$ $2$	$1$ $1$	$- 3$ $- 3$
		$2$ $2$
	$2$ $2$

Step 1.4

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

$1$ $1$	$2$ $2$	$1$ $1$	$- 3$ $- 3$
		$2$ $2$
	$2$ $2$	$3$ $3$

Step 1.5

Multiply the newest entry in the result

(3)

$(3)$ by the divisor

(1)

$(1)$ and place the result of

(3)

$(3)$ under the next term in the dividend

(- 3)

$(- 3)$ .

$1$ $1$	$2$ $2$	$1$ $1$	$- 3$ $- 3$
		$2$ $2$	$3$ $3$
	$2$ $2$	$3$ $3$

Step 1.6

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

$1$ $1$	$2$ $2$	$1$ $1$	$- 3$ $- 3$
		$2$ $2$	$3$ $3$
	$2$ $2$	$3$ $3$	$0$ $0$

Step 1.7

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

(2) x + 3

$(2) x + 3$

Step 1.8

Simplify the quotient polynomial.

2 x + 3

$2 x + 3$

2 x + 3

$2 x + 3$

Step 2

The remainder from dividing

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

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

0

$0$ , which means that

x - 1

$x - 1$ is a factor for

2 x^{2} + x - 3

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

x - 1

$x - 1$ is a factor for

2 x^{2} + x - 3

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

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