Pre-Algebra Examples

$(2 x^{3} - 11 x^{2} + 20 x - 12) \div (x - 2)$

Step 1

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

$x$

$2$

$2 x^{3}$

$11 x^{2}$

$20 x$

$12$

Step 2

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

					$2 x^{2}$
	$x$	-	$2$		$2 x^{3}$	-	$11 x^{2}$	+	$20 x$	-	$12$

Step 3

Multiply the new quotient term by the divisor.

				$2 x^{2}$
$x$	-	$2$		$2 x^{3}$	-	$11 x^{2}$	+	$20 x$	-	$12$
			+	$2 x^{3}$	-	$4 x^{2}$

Step 4

The expression needs to be subtracted from the dividend, so change all the signs in $2 x^{3} - 4 x^{2}$

				$2 x^{2}$
$x$	-	$2$		$2 x^{3}$	-	$11 x^{2}$	+	$20 x$	-	$12$
			-	$2 x^{3}$	+	$4 x^{2}$

Step 5

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

				$2 x^{2}$
$x$	-	$2$		$2 x^{3}$	-	$11 x^{2}$	+	$20 x$	-	$12$
			-	$2 x^{3}$	+	$4 x^{2}$
					-	$7 x^{2}$

Step 6

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

				$2 x^{2}$
$x$	-	$2$		$2 x^{3}$	-	$11 x^{2}$	+	$20 x$	-	$12$
			-	$2 x^{3}$	+	$4 x^{2}$
					-	$7 x^{2}$	+	$20 x$

Step 7

Divide the highest order term in the dividend $- 7 x^{2}$ by the highest order term in divisor $x$ .

				$2 x^{2}$	-	$7 x$
$x$	-	$2$		$2 x^{3}$	-	$11 x^{2}$	+	$20 x$	-	$12$
			-	$2 x^{3}$	+	$4 x^{2}$
					-	$7 x^{2}$	+	$20 x$

Step 8

Multiply the new quotient term by the divisor.

				$2 x^{2}$	-	$7 x$
$x$	-	$2$		$2 x^{3}$	-	$11 x^{2}$	+	$20 x$	-	$12$
			-	$2 x^{3}$	+	$4 x^{2}$
					-	$7 x^{2}$	+	$20 x$
					-	$7 x^{2}$	+	$14 x$

Step 9

The expression needs to be subtracted from the dividend, so change all the signs in $- 7 x^{2} + 14 x$

				$2 x^{2}$	-	$7 x$
$x$	-	$2$		$2 x^{3}$	-	$11 x^{2}$	+	$20 x$	-	$12$
			-	$2 x^{3}$	+	$4 x^{2}$
					-	$7 x^{2}$	+	$20 x$
					+	$7 x^{2}$	-	$14 x$

Step 10

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

				$2 x^{2}$	-	$7 x$
$x$	-	$2$		$2 x^{3}$	-	$11 x^{2}$	+	$20 x$	-	$12$
			-	$2 x^{3}$	+	$4 x^{2}$
					-	$7 x^{2}$	+	$20 x$
					+	$7 x^{2}$	-	$14 x$
							+	$6 x$

Step 11

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

				$2 x^{2}$	-	$7 x$
$x$	-	$2$		$2 x^{3}$	-	$11 x^{2}$	+	$20 x$	-	$12$
			-	$2 x^{3}$	+	$4 x^{2}$
					-	$7 x^{2}$	+	$20 x$
					+	$7 x^{2}$	-	$14 x$
							+	$6 x$	-	$12$

Step 12

Divide the highest order term in the dividend $6 x$ by the highest order term in divisor $x$ .

				$2 x^{2}$	-	$7 x$	+	$6$
$x$	-	$2$		$2 x^{3}$	-	$11 x^{2}$	+	$20 x$	-	$12$
			-	$2 x^{3}$	+	$4 x^{2}$
					-	$7 x^{2}$	+	$20 x$
					+	$7 x^{2}$	-	$14 x$
							+	$6 x$	-	$12$

Step 13

Multiply the new quotient term by the divisor.

				$2 x^{2}$	-	$7 x$	+	$6$
$x$	-	$2$		$2 x^{3}$	-	$11 x^{2}$	+	$20 x$	-	$12$
			-	$2 x^{3}$	+	$4 x^{2}$
					-	$7 x^{2}$	+	$20 x$
					+	$7 x^{2}$	-	$14 x$
							+	$6 x$	-	$12$
							+	$6 x$	-	$12$

Step 14

The expression needs to be subtracted from the dividend, so change all the signs in $6 x - 12$

				$2 x^{2}$	-	$7 x$	+	$6$
$x$	-	$2$		$2 x^{3}$	-	$11 x^{2}$	+	$20 x$	-	$12$
			-	$2 x^{3}$	+	$4 x^{2}$
					-	$7 x^{2}$	+	$20 x$
					+	$7 x^{2}$	-	$14 x$
							+	$6 x$	-	$12$
							-	$6 x$	+	$12$

Step 15

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

				$2 x^{2}$	-	$7 x$	+	$6$
$x$	-	$2$		$2 x^{3}$	-	$11 x^{2}$	+	$20 x$	-	$12$
			-	$2 x^{3}$	+	$4 x^{2}$
					-	$7 x^{2}$	+	$20 x$
					+	$7 x^{2}$	-	$14 x$
							+	$6 x$	-	$12$
							-	$6 x$	+	$12$
										$0$

Step 16

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

$2 x^{2} - 7 x + 6$