Divide (8x^3-22x^2-4)/(4x-3)

$\frac{8 x^{3} - 22 x^{2} - 4}{4 x - 3}$

Step 1

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

$4 x$

$3$

$8 x^{3}$

$22 x^{2}$

$0 x$

$4$

Step 2

Divide the highest order term in the dividend $8 x^{3}$ by the highest order term in divisor $4 x$ .

					$2 x^{2}$
	$4 x$	-	$3$		$8 x^{3}$	-	$22 x^{2}$	+	$0 x$	-	$4$

Step 3

Multiply the new quotient term by the divisor.

				$2 x^{2}$
$4 x$	-	$3$		$8 x^{3}$	-	$22 x^{2}$	+	$0 x$	-	$4$
			+	$8 x^{3}$	-	$6 x^{2}$

Step 4

The expression needs to be subtracted from the dividend, so change all the signs in $8 x^{3} - 6 x^{2}$

				$2 x^{2}$
$4 x$	-	$3$		$8 x^{3}$	-	$22 x^{2}$	+	$0 x$	-	$4$
			-	$8 x^{3}$	+	$6 x^{2}$

Step 5

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

				$2 x^{2}$
$4 x$	-	$3$		$8 x^{3}$	-	$22 x^{2}$	+	$0 x$	-	$4$
			-	$8 x^{3}$	+	$6 x^{2}$
					-	$16 x^{2}$

Step 6

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

				$2 x^{2}$
$4 x$	-	$3$		$8 x^{3}$	-	$22 x^{2}$	+	$0 x$	-	$4$
			-	$8 x^{3}$	+	$6 x^{2}$
					-	$16 x^{2}$	+	$0 x$

Step 7

Divide the highest order term in the dividend $- 16 x^{2}$ by the highest order term in divisor $4 x$ .

				$2 x^{2}$	-	$4 x$
$4 x$	-	$3$		$8 x^{3}$	-	$22 x^{2}$	+	$0 x$	-	$4$
			-	$8 x^{3}$	+	$6 x^{2}$
					-	$16 x^{2}$	+	$0 x$

Step 8

Multiply the new quotient term by the divisor.

				$2 x^{2}$	-	$4 x$
$4 x$	-	$3$		$8 x^{3}$	-	$22 x^{2}$	+	$0 x$	-	$4$
			-	$8 x^{3}$	+	$6 x^{2}$
					-	$16 x^{2}$	+	$0 x$
					-	$16 x^{2}$	+	$12 x$

Step 9

The expression needs to be subtracted from the dividend, so change all the signs in $- 16 x^{2} + 12 x$

				$2 x^{2}$	-	$4 x$
$4 x$	-	$3$		$8 x^{3}$	-	$22 x^{2}$	+	$0 x$	-	$4$
			-	$8 x^{3}$	+	$6 x^{2}$
					-	$16 x^{2}$	+	$0 x$
					+	$16 x^{2}$	-	$12 x$

Step 10

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

				$2 x^{2}$	-	$4 x$
$4 x$	-	$3$		$8 x^{3}$	-	$22 x^{2}$	+	$0 x$	-	$4$
			-	$8 x^{3}$	+	$6 x^{2}$
					-	$16 x^{2}$	+	$0 x$
					+	$16 x^{2}$	-	$12 x$
							-	$12 x$

Step 11

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

				$2 x^{2}$	-	$4 x$
$4 x$	-	$3$		$8 x^{3}$	-	$22 x^{2}$	+	$0 x$	-	$4$
			-	$8 x^{3}$	+	$6 x^{2}$
					-	$16 x^{2}$	+	$0 x$
					+	$16 x^{2}$	-	$12 x$
							-	$12 x$	-	$4$

Step 12

Divide the highest order term in the dividend $- 12 x$ by the highest order term in divisor $4 x$ .

				$2 x^{2}$	-	$4 x$	-	$3$
$4 x$	-	$3$		$8 x^{3}$	-	$22 x^{2}$	+	$0 x$	-	$4$
			-	$8 x^{3}$	+	$6 x^{2}$
					-	$16 x^{2}$	+	$0 x$
					+	$16 x^{2}$	-	$12 x$
							-	$12 x$	-	$4$

Step 13

Multiply the new quotient term by the divisor.

				$2 x^{2}$	-	$4 x$	-	$3$
$4 x$	-	$3$		$8 x^{3}$	-	$22 x^{2}$	+	$0 x$	-	$4$
			-	$8 x^{3}$	+	$6 x^{2}$
					-	$16 x^{2}$	+	$0 x$
					+	$16 x^{2}$	-	$12 x$
							-	$12 x$	-	$4$
							-	$12 x$	+	$9$

Step 14

The expression needs to be subtracted from the dividend, so change all the signs in $- 12 x + 9$

				$2 x^{2}$	-	$4 x$	-	$3$
$4 x$	-	$3$		$8 x^{3}$	-	$22 x^{2}$	+	$0 x$	-	$4$
			-	$8 x^{3}$	+	$6 x^{2}$
					-	$16 x^{2}$	+	$0 x$
					+	$16 x^{2}$	-	$12 x$
							-	$12 x$	-	$4$
							+	$12 x$	-	$9$

Step 15

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

				$2 x^{2}$	-	$4 x$	-	$3$
$4 x$	-	$3$		$8 x^{3}$	-	$22 x^{2}$	+	$0 x$	-	$4$
			-	$8 x^{3}$	+	$6 x^{2}$
					-	$16 x^{2}$	+	$0 x$
					+	$16 x^{2}$	-	$12 x$
							-	$12 x$	-	$4$
							+	$12 x$	-	$9$
									-	$13$

Step 16

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

$2 x^{2} - 4 x - 3 - \frac{13}{4 x - 3}$

Divide (8x^3-22x^2-4)/(4x-3)

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