Divide Using Long Polynomial Division (8x^3-18x^2+11x-21)÷(2x-3)

$(8 x^{3} - 18 x^{2} + 11 x - 21) \div (2 x - 3)$

Step 1

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

$2 x$

$3$

$8 x^{3}$

$18 x^{2}$

$11 x$

$21$

Step 2

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

					$4 x^{2}$
	$2 x$	-	$3$		$8 x^{3}$	-	$18 x^{2}$	+	$11 x$	-	$21$

Step 3

Multiply the new quotient term by the divisor.

				$4 x^{2}$
$2 x$	-	$3$		$8 x^{3}$	-	$18 x^{2}$	+	$11 x$	-	$21$
			+	$8 x^{3}$	-	$12 x^{2}$

Step 4

The expression needs to be subtracted from the dividend, so change all the signs in $8 x^{3} - 12 x^{2}$

				$4 x^{2}$
$2 x$	-	$3$		$8 x^{3}$	-	$18 x^{2}$	+	$11 x$	-	$21$
			-	$8 x^{3}$	+	$12 x^{2}$

Step 5

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

				$4 x^{2}$
$2 x$	-	$3$		$8 x^{3}$	-	$18 x^{2}$	+	$11 x$	-	$21$
			-	$8 x^{3}$	+	$12 x^{2}$
					-	$6 x^{2}$

Step 6

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

				$4 x^{2}$
$2 x$	-	$3$		$8 x^{3}$	-	$18 x^{2}$	+	$11 x$	-	$21$
			-	$8 x^{3}$	+	$12 x^{2}$
					-	$6 x^{2}$	+	$11 x$

Step 7

Divide the highest order term in the dividend $- 6 x^{2}$ by the highest order term in divisor $2 x$ .

				$4 x^{2}$	-	$3 x$
$2 x$	-	$3$		$8 x^{3}$	-	$18 x^{2}$	+	$11 x$	-	$21$
			-	$8 x^{3}$	+	$12 x^{2}$
					-	$6 x^{2}$	+	$11 x$

Step 8

Multiply the new quotient term by the divisor.

				$4 x^{2}$	-	$3 x$
$2 x$	-	$3$		$8 x^{3}$	-	$18 x^{2}$	+	$11 x$	-	$21$
			-	$8 x^{3}$	+	$12 x^{2}$
					-	$6 x^{2}$	+	$11 x$
					-	$6 x^{2}$	+	$9 x$

Step 9

The expression needs to be subtracted from the dividend, so change all the signs in $- 6 x^{2} + 9 x$

				$4 x^{2}$	-	$3 x$
$2 x$	-	$3$		$8 x^{3}$	-	$18 x^{2}$	+	$11 x$	-	$21$
			-	$8 x^{3}$	+	$12 x^{2}$
					-	$6 x^{2}$	+	$11 x$
					+	$6 x^{2}$	-	$9 x$

Step 10

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

				$4 x^{2}$	-	$3 x$
$2 x$	-	$3$		$8 x^{3}$	-	$18 x^{2}$	+	$11 x$	-	$21$
			-	$8 x^{3}$	+	$12 x^{2}$
					-	$6 x^{2}$	+	$11 x$
					+	$6 x^{2}$	-	$9 x$
							+	$2 x$

Step 11

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

				$4 x^{2}$	-	$3 x$
$2 x$	-	$3$		$8 x^{3}$	-	$18 x^{2}$	+	$11 x$	-	$21$
			-	$8 x^{3}$	+	$12 x^{2}$
					-	$6 x^{2}$	+	$11 x$
					+	$6 x^{2}$	-	$9 x$
							+	$2 x$	-	$21$

Step 12

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

				$4 x^{2}$	-	$3 x$	+	$1$
$2 x$	-	$3$		$8 x^{3}$	-	$18 x^{2}$	+	$11 x$	-	$21$
			-	$8 x^{3}$	+	$12 x^{2}$
					-	$6 x^{2}$	+	$11 x$
					+	$6 x^{2}$	-	$9 x$
							+	$2 x$	-	$21$

Step 13

Multiply the new quotient term by the divisor.

				$4 x^{2}$	-	$3 x$	+	$1$
$2 x$	-	$3$		$8 x^{3}$	-	$18 x^{2}$	+	$11 x$	-	$21$
			-	$8 x^{3}$	+	$12 x^{2}$
					-	$6 x^{2}$	+	$11 x$
					+	$6 x^{2}$	-	$9 x$
							+	$2 x$	-	$21$
							+	$2 x$	-	$3$

Step 14

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

				$4 x^{2}$	-	$3 x$	+	$1$
$2 x$	-	$3$		$8 x^{3}$	-	$18 x^{2}$	+	$11 x$	-	$21$
			-	$8 x^{3}$	+	$12 x^{2}$
					-	$6 x^{2}$	+	$11 x$
					+	$6 x^{2}$	-	$9 x$
							+	$2 x$	-	$21$
							-	$2 x$	+	$3$

Step 15

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

				$4 x^{2}$	-	$3 x$	+	$1$
$2 x$	-	$3$		$8 x^{3}$	-	$18 x^{2}$	+	$11 x$	-	$21$
			-	$8 x^{3}$	+	$12 x^{2}$
					-	$6 x^{2}$	+	$11 x$
					+	$6 x^{2}$	-	$9 x$
							+	$2 x$	-	$21$
							-	$2 x$	+	$3$
									-	$18$

Step 16

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

$4 x^{2} - 3 x + 1 - \frac{18}{2 x - 3}$

Divide Using Long Polynomial Division (8x^3-18x^2+11x-21)÷(2x-3)

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