Pre-Algebra Examples

$\frac{8 x^{3} + 18 x^{2} - 4 x + 3}{2 x + 4}$

Step 1

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

$2 x$

$4$

$8 x^{3}$

$18 x^{2}$

$4 x$

$3$

Step 2

Divide the highest order term in the dividend $8 x^{3}$ by the highest order term in divisor $2 x$ .

					$4 x^{2}$
	$2 x$	+	$4$		$8 x^{3}$	+	$18 x^{2}$	-	$4 x$	+	$3$

Step 3

Multiply the new quotient term by the divisor.

				$4 x^{2}$
$2 x$	+	$4$		$8 x^{3}$	+	$18 x^{2}$	-	$4 x$	+	$3$
			+	$8 x^{3}$	+	$16 x^{2}$

Step 4

The expression needs to be subtracted from the dividend, so change all the signs in $8 x^{3} + 16 x^{2}$

				$4 x^{2}$
$2 x$	+	$4$		$8 x^{3}$	+	$18 x^{2}$	-	$4 x$	+	$3$
			-	$8 x^{3}$	-	$16 x^{2}$

Step 5

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

				$4 x^{2}$
$2 x$	+	$4$		$8 x^{3}$	+	$18 x^{2}$	-	$4 x$	+	$3$
			-	$8 x^{3}$	-	$16 x^{2}$
					+	$2 x^{2}$

Step 6

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

				$4 x^{2}$
$2 x$	+	$4$		$8 x^{3}$	+	$18 x^{2}$	-	$4 x$	+	$3$
			-	$8 x^{3}$	-	$16 x^{2}$
					+	$2 x^{2}$	-	$4 x$

Step 7

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

				$4 x^{2}$	+	$x$
$2 x$	+	$4$		$8 x^{3}$	+	$18 x^{2}$	-	$4 x$	+	$3$
			-	$8 x^{3}$	-	$16 x^{2}$
					+	$2 x^{2}$	-	$4 x$

Step 8

Multiply the new quotient term by the divisor.

				$4 x^{2}$	+	$x$
$2 x$	+	$4$		$8 x^{3}$	+	$18 x^{2}$	-	$4 x$	+	$3$
			-	$8 x^{3}$	-	$16 x^{2}$
					+	$2 x^{2}$	-	$4 x$
					+	$2 x^{2}$	+	$4 x$

Step 9

The expression needs to be subtracted from the dividend, so change all the signs in $2 x^{2} + 4 x$

				$4 x^{2}$	+	$x$
$2 x$	+	$4$		$8 x^{3}$	+	$18 x^{2}$	-	$4 x$	+	$3$
			-	$8 x^{3}$	-	$16 x^{2}$
					+	$2 x^{2}$	-	$4 x$
					-	$2 x^{2}$	-	$4 x$

Step 10

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

				$4 x^{2}$	+	$x$
$2 x$	+	$4$		$8 x^{3}$	+	$18 x^{2}$	-	$4 x$	+	$3$
			-	$8 x^{3}$	-	$16 x^{2}$
					+	$2 x^{2}$	-	$4 x$
					-	$2 x^{2}$	-	$4 x$
							-	$8 x$

Step 11

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

				$4 x^{2}$	+	$x$
$2 x$	+	$4$		$8 x^{3}$	+	$18 x^{2}$	-	$4 x$	+	$3$
			-	$8 x^{3}$	-	$16 x^{2}$
					+	$2 x^{2}$	-	$4 x$
					-	$2 x^{2}$	-	$4 x$
							-	$8 x$	+	$3$

Step 12

Divide the highest order term in the dividend $- 8 x$ by the highest order term in divisor $2 x$ .

				$4 x^{2}$	+	$x$	-	$4$
$2 x$	+	$4$		$8 x^{3}$	+	$18 x^{2}$	-	$4 x$	+	$3$
			-	$8 x^{3}$	-	$16 x^{2}$
					+	$2 x^{2}$	-	$4 x$
					-	$2 x^{2}$	-	$4 x$
							-	$8 x$	+	$3$

Step 13

Multiply the new quotient term by the divisor.

				$4 x^{2}$	+	$x$	-	$4$
$2 x$	+	$4$		$8 x^{3}$	+	$18 x^{2}$	-	$4 x$	+	$3$
			-	$8 x^{3}$	-	$16 x^{2}$
					+	$2 x^{2}$	-	$4 x$
					-	$2 x^{2}$	-	$4 x$
							-	$8 x$	+	$3$
							-	$8 x$	-	$16$

Step 14

The expression needs to be subtracted from the dividend, so change all the signs in $- 8 x - 16$

				$4 x^{2}$	+	$x$	-	$4$
$2 x$	+	$4$		$8 x^{3}$	+	$18 x^{2}$	-	$4 x$	+	$3$
			-	$8 x^{3}$	-	$16 x^{2}$
					+	$2 x^{2}$	-	$4 x$
					-	$2 x^{2}$	-	$4 x$
							-	$8 x$	+	$3$
							+	$8 x$	+	$16$

Step 15

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

				$4 x^{2}$	+	$x$	-	$4$
$2 x$	+	$4$		$8 x^{3}$	+	$18 x^{2}$	-	$4 x$	+	$3$
			-	$8 x^{3}$	-	$16 x^{2}$
					+	$2 x^{2}$	-	$4 x$
					-	$2 x^{2}$	-	$4 x$
							-	$8 x$	+	$3$
							+	$8 x$	+	$16$
									+	$19$

Step 16

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

$4 x^{2} + x - 4 + \frac{19}{2 x + 4}$