Divide Using Long Polynomial Division (11x-20x^2+12x^3-14)/(x-2)

$\frac{11 x - 20 x^{2} + 12 x^{3} - 14}{x - 2}$

Step 1

Expand $11 x - 20 x^{2} + 12 x^{3} - 14$ .

Reorder $11 x$ and $- 20 x^{2}$ .

$\frac{- 20 x^{2} + 11 x + 12 x^{3} - 14}{x - 2}$

Move $11 x$ .

$\frac{- 20 x^{2} + 12 x^{3} + 11 x - 14}{x - 2}$

Reorder $- 20 x^{2}$ and $12 x^{3}$ .

$\frac{12 x^{3} - 20 x^{2} + 11 x - 14}{x - 2}$

Step 2

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

$x$

$2$

$12 x^{3}$

$20 x^{2}$

$11 x$

$14$

Step 3

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

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

Step 4

Multiply the new quotient term by the divisor.

				$12 x^{2}$
$x$	-	$2$		$12 x^{3}$	-	$20 x^{2}$	+	$11 x$	-	$14$
			+	$12 x^{3}$	-	$24 x^{2}$

Step 5

The expression needs to be subtracted from the dividend, so change all the signs in $12 x^{3} - 24 x^{2}$

				$12 x^{2}$
$x$	-	$2$		$12 x^{3}$	-	$20 x^{2}$	+	$11 x$	-	$14$
			-	$12 x^{3}$	+	$24 x^{2}$

Step 6

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

				$12 x^{2}$
$x$	-	$2$		$12 x^{3}$	-	$20 x^{2}$	+	$11 x$	-	$14$
			-	$12 x^{3}$	+	$24 x^{2}$
					+	$4 x^{2}$

Step 7

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

				$12 x^{2}$
$x$	-	$2$		$12 x^{3}$	-	$20 x^{2}$	+	$11 x$	-	$14$
			-	$12 x^{3}$	+	$24 x^{2}$
					+	$4 x^{2}$	+	$11 x$

Step 8

Divide the highest order term in the dividend $4 x^{2}$ by the highest order term in divisor $x$ .

				$12 x^{2}$	+	$4 x$
$x$	-	$2$		$12 x^{3}$	-	$20 x^{2}$	+	$11 x$	-	$14$
			-	$12 x^{3}$	+	$24 x^{2}$
					+	$4 x^{2}$	+	$11 x$

Step 9

Multiply the new quotient term by the divisor.

				$12 x^{2}$	+	$4 x$
$x$	-	$2$		$12 x^{3}$	-	$20 x^{2}$	+	$11 x$	-	$14$
			-	$12 x^{3}$	+	$24 x^{2}$
					+	$4 x^{2}$	+	$11 x$
					+	$4 x^{2}$	-	$8 x$

Step 10

The expression needs to be subtracted from the dividend, so change all the signs in $4 x^{2} - 8 x$

				$12 x^{2}$	+	$4 x$
$x$	-	$2$		$12 x^{3}$	-	$20 x^{2}$	+	$11 x$	-	$14$
			-	$12 x^{3}$	+	$24 x^{2}$
					+	$4 x^{2}$	+	$11 x$
					-	$4 x^{2}$	+	$8 x$

Step 11

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

				$12 x^{2}$	+	$4 x$
$x$	-	$2$		$12 x^{3}$	-	$20 x^{2}$	+	$11 x$	-	$14$
			-	$12 x^{3}$	+	$24 x^{2}$
					+	$4 x^{2}$	+	$11 x$
					-	$4 x^{2}$	+	$8 x$
							+	$19 x$

Step 12

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

				$12 x^{2}$	+	$4 x$
$x$	-	$2$		$12 x^{3}$	-	$20 x^{2}$	+	$11 x$	-	$14$
			-	$12 x^{3}$	+	$24 x^{2}$
					+	$4 x^{2}$	+	$11 x$
					-	$4 x^{2}$	+	$8 x$
							+	$19 x$	-	$14$

Step 13

Divide the highest order term in the dividend $19 x$ by the highest order term in divisor $x$ .

				$12 x^{2}$	+	$4 x$	+	$19$
$x$	-	$2$		$12 x^{3}$	-	$20 x^{2}$	+	$11 x$	-	$14$
			-	$12 x^{3}$	+	$24 x^{2}$
					+	$4 x^{2}$	+	$11 x$
					-	$4 x^{2}$	+	$8 x$
							+	$19 x$	-	$14$

Step 14

Multiply the new quotient term by the divisor.

				$12 x^{2}$	+	$4 x$	+	$19$
$x$	-	$2$		$12 x^{3}$	-	$20 x^{2}$	+	$11 x$	-	$14$
			-	$12 x^{3}$	+	$24 x^{2}$
					+	$4 x^{2}$	+	$11 x$
					-	$4 x^{2}$	+	$8 x$
							+	$19 x$	-	$14$
							+	$19 x$	-	$38$

Step 15

The expression needs to be subtracted from the dividend, so change all the signs in $19 x - 38$

				$12 x^{2}$	+	$4 x$	+	$19$
$x$	-	$2$		$12 x^{3}$	-	$20 x^{2}$	+	$11 x$	-	$14$
			-	$12 x^{3}$	+	$24 x^{2}$
					+	$4 x^{2}$	+	$11 x$
					-	$4 x^{2}$	+	$8 x$
							+	$19 x$	-	$14$
							-	$19 x$	+	$38$

Step 16

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

				$12 x^{2}$	+	$4 x$	+	$19$
$x$	-	$2$		$12 x^{3}$	-	$20 x^{2}$	+	$11 x$	-	$14$
			-	$12 x^{3}$	+	$24 x^{2}$
					+	$4 x^{2}$	+	$11 x$
					-	$4 x^{2}$	+	$8 x$
							+	$19 x$	-	$14$
							-	$19 x$	+	$38$
									+	$24$

Step 17

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

$12 x^{2} + 4 x + 19 + \frac{24}{x - 2}$

Divide Using Long Polynomial Division (11x-20x^2+12x^3-14)/(x-2)

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