Examples

$x^{2} - 1$ ,

$x + 1$

Step 1

Divide the first expression by the second expression.

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

Step 2

Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of

$0$ .

$x$

$1$

$x^{2}$

$0 x$

$1$

Step 3

Divide the highest order term in the dividend

$x^{2}$ by the highest order term in divisor

$x$ .

					$x$
	$x$	+	$1$		$x^{2}$	+	$0 x$	-	$1$

Step 4

Multiply the new quotient term by the divisor.

				$x$
$x$	+	$1$		$x^{2}$	+	$0 x$	-	$1$
			+	$x^{2}$	+	$x$

Step 5

The expression needs to be subtracted from the dividend, so change all the signs in

$x^{2} + x$

				$x$
$x$	+	$1$		$x^{2}$	+	$0 x$	-	$1$
			-	$x^{2}$	-	$x$

Step 6

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

				$x$
$x$	+	$1$		$x^{2}$	+	$0 x$	-	$1$
			-	$x^{2}$	-	$x$
					-	$x$

Step 7

Pull the next terms from the original dividend down into the current dividend.

				$x$
$x$	+	$1$		$x^{2}$	+	$0 x$	-	$1$
			-	$x^{2}$	-	$x$
					-	$x$	-	$1$

Step 8

Divide the highest order term in the dividend

$- x$ by the highest order term in divisor

$x$ .

				$x$	-	$1$
$x$	+	$1$		$x^{2}$	+	$0 x$	-	$1$
			-	$x^{2}$	-	$x$
					-	$x$	-	$1$

Step 9

Multiply the new quotient term by the divisor.

				$x$	-	$1$
$x$	+	$1$		$x^{2}$	+	$0 x$	-	$1$
			-	$x^{2}$	-	$x$
					-	$x$	-	$1$
					-	$x$	-	$1$

Step 10

The expression needs to be subtracted from the dividend, so change all the signs in

$- x - 1$

				$x$	-	$1$
$x$	+	$1$		$x^{2}$	+	$0 x$	-	$1$
			-	$x^{2}$	-	$x$
					-	$x$	-	$1$
					+	$x$	+	$1$

Step 11

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

				$x$	-	$1$
$x$	+	$1$		$x^{2}$	+	$0 x$	-	$1$
			-	$x^{2}$	-	$x$
					-	$x$	-	$1$
					+	$x$	+	$1$
								$0$

Step 12

Since the remainder is

$0$ , the final answer is the quotient.

$x - 1$

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