Pre-Algebra Examples Simplifying and Evaluating Expressions

Divide

$6 x^{3} + 12 x^{2} - 18$ , $3 x$

Step 1

Divide the first expression by the second expression.

$\frac{6 x^{3} + 12 x^{2} - 18}{3 x}$

Step 2

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

$3 x$

$0$

$6 x^{3}$

$12 x^{2}$

$0 x$

$18$

Step 3

Divide the highest order term in the dividend $6 x^{3}$ by the highest order term in divisor $3 x$ .

					$2 x^{2}$
	$3 x$	+	$0$		$6 x^{3}$	+	$12 x^{2}$	+	$0 x$	-	$18$

Step 4

Multiply the new quotient term by the divisor.

				$2 x^{2}$
$3 x$	+	$0$		$6 x^{3}$	+	$12 x^{2}$	+	$0 x$	-	$18$
			+	$6 x^{3}$	+	$0$

Step 5

The expression needs to be subtracted from the dividend, so change all the signs in $6 x^{3} + 0$

				$2 x^{2}$
$3 x$	+	$0$		$6 x^{3}$	+	$12 x^{2}$	+	$0 x$	-	$18$
			-	$6 x^{3}$	-	$0$

Step 6

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

				$2 x^{2}$
$3 x$	+	$0$		$6 x^{3}$	+	$12 x^{2}$	+	$0 x$	-	$18$
			-	$6 x^{3}$	-	$0$
					+	$12 x^{2}$

Step 7

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

				$2 x^{2}$
$3 x$	+	$0$		$6 x^{3}$	+	$12 x^{2}$	+	$0 x$	-	$18$
			-	$6 x^{3}$	-	$0$
					+	$12 x^{2}$	+	$0 x$

Step 8

Divide the highest order term in the dividend $12 x^{2}$ by the highest order term in divisor $3 x$ .

				$2 x^{2}$	+	$4 x$
$3 x$	+	$0$		$6 x^{3}$	+	$12 x^{2}$	+	$0 x$	-	$18$
			-	$6 x^{3}$	-	$0$
					+	$12 x^{2}$	+	$0 x$

Step 9

Multiply the new quotient term by the divisor.

				$2 x^{2}$	+	$4 x$
$3 x$	+	$0$		$6 x^{3}$	+	$12 x^{2}$	+	$0 x$	-	$18$
			-	$6 x^{3}$	-	$0$
					+	$12 x^{2}$	+	$0 x$
					+	$12 x^{2}$	+	$0$

Step 10

The expression needs to be subtracted from the dividend, so change all the signs in $12 x^{2} + 0$

				$2 x^{2}$	+	$4 x$
$3 x$	+	$0$		$6 x^{3}$	+	$12 x^{2}$	+	$0 x$	-	$18$
			-	$6 x^{3}$	-	$0$
					+	$12 x^{2}$	+	$0 x$
					-	$12 x^{2}$	-	$0$

Step 11

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

				$2 x^{2}$	+	$4 x$
$3 x$	+	$0$		$6 x^{3}$	+	$12 x^{2}$	+	$0 x$	-	$18$
			-	$6 x^{3}$	-	$0$
					+	$12 x^{2}$	+	$0 x$
					-	$12 x^{2}$	-	$0$
								$0$

Step 12

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

				$2 x^{2}$	+	$4 x$
$3 x$	+	$0$		$6 x^{3}$	+	$12 x^{2}$	+	$0 x$	-	$18$
			-	$6 x^{3}$	-	$0$
					+	$12 x^{2}$	+	$0 x$
					-	$12 x^{2}$	-	$0$
								$0$	-	$18$

Step 13

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

$2 x^{2} + 4 x - \frac{18}{3 x}$

Enter YOUR Problem

Divide

Simplifying and Evaluating Expressions

How to Use Step-by-Step Examples

Why use Mathway?

Explore More Pre-Algebra Help