Algebra Examples

x^{2} - 5 x + 6

$x^{2} - 5 x + 6$ ,

x + 6

$x + 6$

Step 1

Divide the first expression by the second expression.

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

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

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

$x$

6

$6$

x^{2}

$x^{2}$

5 x

$5 x$

6

$6$

Step 3

Divide the highest order term in the dividend

x^{2}

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

x

$x$ .

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

Step 4

Multiply the new quotient term by the divisor.

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

Step 5

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

x^{2} + 6 x

$x^{2} + 6 x$

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

Step 6

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

				$x$ $x$
$x$ $x$	+	$6$ $6$		$x^{2}$ $x^{2}$	-	$5 x$ $5 x$	+	$6$ $6$
			-	$x^{2}$ $x^{2}$	-	$6 x$ $6 x$
					-	$11 x$ $11 x$

Step 7

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

				$x$ $x$
$x$ $x$	+	$6$ $6$		$x^{2}$ $x^{2}$	-	$5 x$ $5 x$	+	$6$ $6$
			-	$x^{2}$ $x^{2}$	-	$6 x$ $6 x$
					-	$11 x$ $11 x$	+	$6$ $6$

Step 8

Divide the highest order term in the dividend

- 11 x

$- 11 x$ by the highest order term in divisor

x

$x$ .

				$x$ $x$	-	$11$ $11$
$x$ $x$	+	$6$ $6$		$x^{2}$ $x^{2}$	-	$5 x$ $5 x$	+	$6$ $6$
			-	$x^{2}$ $x^{2}$	-	$6 x$ $6 x$
					-	$11 x$ $11 x$	+	$6$ $6$

Step 9

Multiply the new quotient term by the divisor.

				$x$ $x$	-	$11$ $11$
$x$ $x$	+	$6$ $6$		$x^{2}$ $x^{2}$	-	$5 x$ $5 x$	+	$6$ $6$
			-	$x^{2}$ $x^{2}$	-	$6 x$ $6 x$
					-	$11 x$ $11 x$	+	$6$ $6$
					-	$11 x$ $11 x$	-	$66$ $66$

Step 10

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

- 11 x - 66

$- 11 x - 66$

				$x$ $x$	-	$11$ $11$
$x$ $x$	+	$6$ $6$		$x^{2}$ $x^{2}$	-	$5 x$ $5 x$	+	$6$ $6$
			-	$x^{2}$ $x^{2}$	-	$6 x$ $6 x$
					-	$11 x$ $11 x$	+	$6$ $6$
					+	$11 x$ $11 x$	+	$66$ $66$

Step 11

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

				$x$ $x$	-	$11$ $11$
$x$ $x$	+	$6$ $6$		$x^{2}$ $x^{2}$	-	$5 x$ $5 x$	+	$6$ $6$
			-	$x^{2}$ $x^{2}$	-	$6 x$ $6 x$
					-	$11 x$ $11 x$	+	$6$ $6$
					+	$11 x$ $11 x$	+	$66$ $66$
							+	$72$ $72$

Step 12

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

x - 11 + \frac{72}{x + 6}

$x - 11 + \frac{72}{x + 6}$

Enter YOUR Problem