Examples

12 x^{2} - 64 x - 11

$12 x^{2} - 64 x - 11$ ,

x + 1

$x + 1$

Step 1

Divide the first expression by the second expression.

\frac{12 x^{2} - 64 x - 11}{x + 1}

$\frac{12 x^{2} - 64 x - 11}{x + 1}$

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

$0$ .

x

$x$

1

$1$

12 x^{2}

$12 x^{2}$

64 x

$64 x$

11

$11$

Step 3

Divide the highest order term in the dividend

12 x^{2}

$12 x^{2}$ by the highest order term in divisor

x

$x$ .

					$12 x$ $12 x$
	$x$ $x$	+	$1$ $1$		$12 x^{2}$ $12 x^{2}$	-	$64 x$ $64 x$	-	$11$ $11$

Step 4

Multiply the new quotient term by the divisor.

				$12 x$ $12 x$
$x$ $x$	+	$1$ $1$		$12 x^{2}$ $12 x^{2}$	-	$64 x$ $64 x$	-	$11$ $11$
			+	$12 x^{2}$ $12 x^{2}$	+	$12 x$ $12 x$

Step 5

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

12 x^{2} + 12 x

$12 x^{2} + 12 x$

				$12 x$ $12 x$
$x$ $x$	+	$1$ $1$		$12 x^{2}$ $12 x^{2}$	-	$64 x$ $64 x$	-	$11$ $11$
			-	$12 x^{2}$ $12 x^{2}$	-	$12 x$ $12 x$

Step 6

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

				$12 x$ $12 x$
$x$ $x$	+	$1$ $1$		$12 x^{2}$ $12 x^{2}$	-	$64 x$ $64 x$	-	$11$ $11$
			-	$12 x^{2}$ $12 x^{2}$	-	$12 x$ $12 x$
					-	$76 x$ $76 x$

Step 7

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

				$12 x$ $12 x$
$x$ $x$	+	$1$ $1$		$12 x^{2}$ $12 x^{2}$	-	$64 x$ $64 x$	-	$11$ $11$
			-	$12 x^{2}$ $12 x^{2}$	-	$12 x$ $12 x$
					-	$76 x$ $76 x$	-	$11$ $11$

Step 8

Divide the highest order term in the dividend

- 76 x

$- 76 x$ by the highest order term in divisor

x

$x$ .

				$12 x$ $12 x$	-	$76$ $76$
$x$ $x$	+	$1$ $1$		$12 x^{2}$ $12 x^{2}$	-	$64 x$ $64 x$	-	$11$ $11$
			-	$12 x^{2}$ $12 x^{2}$	-	$12 x$ $12 x$
					-	$76 x$ $76 x$	-	$11$ $11$

Step 9

Multiply the new quotient term by the divisor.

				$12 x$ $12 x$	-	$76$ $76$
$x$ $x$	+	$1$ $1$		$12 x^{2}$ $12 x^{2}$	-	$64 x$ $64 x$	-	$11$ $11$
			-	$12 x^{2}$ $12 x^{2}$	-	$12 x$ $12 x$
					-	$76 x$ $76 x$	-	$11$ $11$
					-	$76 x$ $76 x$	-	$76$ $76$

Step 10

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

- 76 x - 76

$- 76 x - 76$

				$12 x$ $12 x$	-	$76$ $76$
$x$ $x$	+	$1$ $1$		$12 x^{2}$ $12 x^{2}$	-	$64 x$ $64 x$	-	$11$ $11$
			-	$12 x^{2}$ $12 x^{2}$	-	$12 x$ $12 x$
					-	$76 x$ $76 x$	-	$11$ $11$
					+	$76 x$ $76 x$	+	$76$ $76$

Step 11

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

				$12 x$ $12 x$	-	$76$ $76$
$x$ $x$	+	$1$ $1$		$12 x^{2}$ $12 x^{2}$	-	$64 x$ $64 x$	-	$11$ $11$
			-	$12 x^{2}$ $12 x^{2}$	-	$12 x$ $12 x$
					-	$76 x$ $76 x$	-	$11$ $11$
					+	$76 x$ $76 x$	+	$76$ $76$
							+	$65$ $65$

Step 12

The final answer is the quotient plus the remainder over the divisor.

12 x - 76 + \frac{65}{x + 1}

$12 x - 76 + \frac{65}{x + 1}$

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