Pre-Algebra Examples

$\frac{18 x^{3} - 37 x^{2} - 101 x - 36}{9 x + 4}$

Step 1

Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of $0$ .

$9 x$

$4$

$18 x^{3}$

$37 x^{2}$

$101 x$

$36$

Step 2

Divide the highest order term in the dividend $18 x^{3}$ by the highest order term in divisor $9 x$ .

					$2 x^{2}$
	$9 x$	+	$4$		$18 x^{3}$	-	$37 x^{2}$	-	$101 x$	-	$36$

Step 3

Multiply the new quotient term by the divisor.

				$2 x^{2}$
$9 x$	+	$4$		$18 x^{3}$	-	$37 x^{2}$	-	$101 x$	-	$36$
			+	$18 x^{3}$	+	$8 x^{2}$

Step 4

The expression needs to be subtracted from the dividend, so change all the signs in $18 x^{3} + 8 x^{2}$

				$2 x^{2}$
$9 x$	+	$4$		$18 x^{3}$	-	$37 x^{2}$	-	$101 x$	-	$36$
			-	$18 x^{3}$	-	$8 x^{2}$

Step 5

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

				$2 x^{2}$
$9 x$	+	$4$		$18 x^{3}$	-	$37 x^{2}$	-	$101 x$	-	$36$
			-	$18 x^{3}$	-	$8 x^{2}$
					-	$45 x^{2}$

Step 6

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

				$2 x^{2}$
$9 x$	+	$4$		$18 x^{3}$	-	$37 x^{2}$	-	$101 x$	-	$36$
			-	$18 x^{3}$	-	$8 x^{2}$
					-	$45 x^{2}$	-	$101 x$

Step 7

Divide the highest order term in the dividend $- 45 x^{2}$ by the highest order term in divisor $9 x$ .

				$2 x^{2}$	-	$5 x$
$9 x$	+	$4$		$18 x^{3}$	-	$37 x^{2}$	-	$101 x$	-	$36$
			-	$18 x^{3}$	-	$8 x^{2}$
					-	$45 x^{2}$	-	$101 x$

Step 8

Multiply the new quotient term by the divisor.

				$2 x^{2}$	-	$5 x$
$9 x$	+	$4$		$18 x^{3}$	-	$37 x^{2}$	-	$101 x$	-	$36$
			-	$18 x^{3}$	-	$8 x^{2}$
					-	$45 x^{2}$	-	$101 x$
					-	$45 x^{2}$	-	$20 x$

Step 9

The expression needs to be subtracted from the dividend, so change all the signs in $- 45 x^{2} - 20 x$

				$2 x^{2}$	-	$5 x$
$9 x$	+	$4$		$18 x^{3}$	-	$37 x^{2}$	-	$101 x$	-	$36$
			-	$18 x^{3}$	-	$8 x^{2}$
					-	$45 x^{2}$	-	$101 x$
					+	$45 x^{2}$	+	$20 x$

Step 10

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

				$2 x^{2}$	-	$5 x$
$9 x$	+	$4$		$18 x^{3}$	-	$37 x^{2}$	-	$101 x$	-	$36$
			-	$18 x^{3}$	-	$8 x^{2}$
					-	$45 x^{2}$	-	$101 x$
					+	$45 x^{2}$	+	$20 x$
							-	$81 x$

Step 11

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

				$2 x^{2}$	-	$5 x$
$9 x$	+	$4$		$18 x^{3}$	-	$37 x^{2}$	-	$101 x$	-	$36$
			-	$18 x^{3}$	-	$8 x^{2}$
					-	$45 x^{2}$	-	$101 x$
					+	$45 x^{2}$	+	$20 x$
							-	$81 x$	-	$36$

Step 12

Divide the highest order term in the dividend $- 81 x$ by the highest order term in divisor $9 x$ .

				$2 x^{2}$	-	$5 x$	-	$9$
$9 x$	+	$4$		$18 x^{3}$	-	$37 x^{2}$	-	$101 x$	-	$36$
			-	$18 x^{3}$	-	$8 x^{2}$
					-	$45 x^{2}$	-	$101 x$
					+	$45 x^{2}$	+	$20 x$
							-	$81 x$	-	$36$

Step 13

Multiply the new quotient term by the divisor.

				$2 x^{2}$	-	$5 x$	-	$9$
$9 x$	+	$4$		$18 x^{3}$	-	$37 x^{2}$	-	$101 x$	-	$36$
			-	$18 x^{3}$	-	$8 x^{2}$
					-	$45 x^{2}$	-	$101 x$
					+	$45 x^{2}$	+	$20 x$
							-	$81 x$	-	$36$
							-	$81 x$	-	$36$

Step 14

The expression needs to be subtracted from the dividend, so change all the signs in $- 81 x - 36$

				$2 x^{2}$	-	$5 x$	-	$9$
$9 x$	+	$4$		$18 x^{3}$	-	$37 x^{2}$	-	$101 x$	-	$36$
			-	$18 x^{3}$	-	$8 x^{2}$
					-	$45 x^{2}$	-	$101 x$
					+	$45 x^{2}$	+	$20 x$
							-	$81 x$	-	$36$
							+	$81 x$	+	$36$

Step 15

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

				$2 x^{2}$	-	$5 x$	-	$9$
$9 x$	+	$4$		$18 x^{3}$	-	$37 x^{2}$	-	$101 x$	-	$36$
			-	$18 x^{3}$	-	$8 x^{2}$
					-	$45 x^{2}$	-	$101 x$
					+	$45 x^{2}$	+	$20 x$
							-	$81 x$	-	$36$
							+	$81 x$	+	$36$
										$0$

Step 16

Since the remander is $0$ , the final answer is the quotient.

$2 x^{2} - 5 x - 9$