Divide Using Long Polynomial Division (8x^3+18x^2+7x-3)÷(4x-1)

$(8 x^{3} + 18 x^{2} + 7 x - 3) \div (4 x - 1)$

Step 1

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

$4 x$

$1$

$8 x^{3}$

$18 x^{2}$

$7 x$

$3$

Step 2

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

					$2 x^{2}$
	$4 x$	-	$1$		$8 x^{3}$	+	$18 x^{2}$	+	$7 x$	-	$3$

Step 3

Multiply the new quotient term by the divisor.

				$2 x^{2}$
$4 x$	-	$1$		$8 x^{3}$	+	$18 x^{2}$	+	$7 x$	-	$3$
			+	$8 x^{3}$	-	$2 x^{2}$

Step 4

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

				$2 x^{2}$
$4 x$	-	$1$		$8 x^{3}$	+	$18 x^{2}$	+	$7 x$	-	$3$
			-	$8 x^{3}$	+	$2 x^{2}$

Step 5

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

				$2 x^{2}$
$4 x$	-	$1$		$8 x^{3}$	+	$18 x^{2}$	+	$7 x$	-	$3$
			-	$8 x^{3}$	+	$2 x^{2}$
					+	$20 x^{2}$

Step 6

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

				$2 x^{2}$
$4 x$	-	$1$		$8 x^{3}$	+	$18 x^{2}$	+	$7 x$	-	$3$
			-	$8 x^{3}$	+	$2 x^{2}$
					+	$20 x^{2}$	+	$7 x$

Step 7

Divide the highest order term in the dividend $20 x^{2}$ by the highest order term in divisor $4 x$ .

				$2 x^{2}$	+	$5 x$
$4 x$	-	$1$		$8 x^{3}$	+	$18 x^{2}$	+	$7 x$	-	$3$
			-	$8 x^{3}$	+	$2 x^{2}$
					+	$20 x^{2}$	+	$7 x$

Step 8

Multiply the new quotient term by the divisor.

				$2 x^{2}$	+	$5 x$
$4 x$	-	$1$		$8 x^{3}$	+	$18 x^{2}$	+	$7 x$	-	$3$
			-	$8 x^{3}$	+	$2 x^{2}$
					+	$20 x^{2}$	+	$7 x$
					+	$20 x^{2}$	-	$5 x$

Step 9

The expression needs to be subtracted from the dividend, so change all the signs in $20 x^{2} - 5 x$

				$2 x^{2}$	+	$5 x$
$4 x$	-	$1$		$8 x^{3}$	+	$18 x^{2}$	+	$7 x$	-	$3$
			-	$8 x^{3}$	+	$2 x^{2}$
					+	$20 x^{2}$	+	$7 x$
					-	$20 x^{2}$	+	$5 x$

Step 10

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

				$2 x^{2}$	+	$5 x$
$4 x$	-	$1$		$8 x^{3}$	+	$18 x^{2}$	+	$7 x$	-	$3$
			-	$8 x^{3}$	+	$2 x^{2}$
					+	$20 x^{2}$	+	$7 x$
					-	$20 x^{2}$	+	$5 x$
							+	$12 x$

Step 11

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

				$2 x^{2}$	+	$5 x$
$4 x$	-	$1$		$8 x^{3}$	+	$18 x^{2}$	+	$7 x$	-	$3$
			-	$8 x^{3}$	+	$2 x^{2}$
					+	$20 x^{2}$	+	$7 x$
					-	$20 x^{2}$	+	$5 x$
							+	$12 x$	-	$3$

Step 12

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

				$2 x^{2}$	+	$5 x$	+	$3$
$4 x$	-	$1$		$8 x^{3}$	+	$18 x^{2}$	+	$7 x$	-	$3$
			-	$8 x^{3}$	+	$2 x^{2}$
					+	$20 x^{2}$	+	$7 x$
					-	$20 x^{2}$	+	$5 x$
							+	$12 x$	-	$3$

Step 13

Multiply the new quotient term by the divisor.

				$2 x^{2}$	+	$5 x$	+	$3$
$4 x$	-	$1$		$8 x^{3}$	+	$18 x^{2}$	+	$7 x$	-	$3$
			-	$8 x^{3}$	+	$2 x^{2}$
					+	$20 x^{2}$	+	$7 x$
					-	$20 x^{2}$	+	$5 x$
							+	$12 x$	-	$3$
							+	$12 x$	-	$3$

Step 14

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

				$2 x^{2}$	+	$5 x$	+	$3$
$4 x$	-	$1$		$8 x^{3}$	+	$18 x^{2}$	+	$7 x$	-	$3$
			-	$8 x^{3}$	+	$2 x^{2}$
					+	$20 x^{2}$	+	$7 x$
					-	$20 x^{2}$	+	$5 x$
							+	$12 x$	-	$3$
							-	$12 x$	+	$3$

Step 15

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

				$2 x^{2}$	+	$5 x$	+	$3$
$4 x$	-	$1$		$8 x^{3}$	+	$18 x^{2}$	+	$7 x$	-	$3$
			-	$8 x^{3}$	+	$2 x^{2}$
					+	$20 x^{2}$	+	$7 x$
					-	$20 x^{2}$	+	$5 x$
							+	$12 x$	-	$3$
							-	$12 x$	+	$3$
										$0$

Step 16

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

$2 x^{2} + 5 x + 3$

Divide Using Long Polynomial Division (8x^3+18x^2+7x-3)÷(4x-1)

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