Divide Using Long Polynomial Division (6x^3-11x^2-47x-20)÷(2x+1)

$(6 x^{3} - 11 x^{2} - 47 x - 20) \div (2 x + 1)$

Step 1

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

$2 x$

$1$

$6 x^{3}$

$11 x^{2}$

$47 x$

$20$

Step 2

Divide the highest order term in the dividend $6 x^{3}$ by the highest order term in divisor $2 x$ .

					$3 x^{2}$
	$2 x$	+	$1$		$6 x^{3}$	-	$11 x^{2}$	-	$47 x$	-	$20$

Step 3

Multiply the new quotient term by the divisor.

				$3 x^{2}$
$2 x$	+	$1$		$6 x^{3}$	-	$11 x^{2}$	-	$47 x$	-	$20$
			+	$6 x^{3}$	+	$3 x^{2}$

Step 4

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

				$3 x^{2}$
$2 x$	+	$1$		$6 x^{3}$	-	$11 x^{2}$	-	$47 x$	-	$20$
			-	$6 x^{3}$	-	$3 x^{2}$

Step 5

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

				$3 x^{2}$
$2 x$	+	$1$		$6 x^{3}$	-	$11 x^{2}$	-	$47 x$	-	$20$
			-	$6 x^{3}$	-	$3 x^{2}$
					-	$14 x^{2}$

Step 6

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

				$3 x^{2}$
$2 x$	+	$1$		$6 x^{3}$	-	$11 x^{2}$	-	$47 x$	-	$20$
			-	$6 x^{3}$	-	$3 x^{2}$
					-	$14 x^{2}$	-	$47 x$

Step 7

Divide the highest order term in the dividend $- 14 x^{2}$ by the highest order term in divisor $2 x$ .

				$3 x^{2}$	-	$7 x$
$2 x$	+	$1$		$6 x^{3}$	-	$11 x^{2}$	-	$47 x$	-	$20$
			-	$6 x^{3}$	-	$3 x^{2}$
					-	$14 x^{2}$	-	$47 x$

Step 8

Multiply the new quotient term by the divisor.

				$3 x^{2}$	-	$7 x$
$2 x$	+	$1$		$6 x^{3}$	-	$11 x^{2}$	-	$47 x$	-	$20$
			-	$6 x^{3}$	-	$3 x^{2}$
					-	$14 x^{2}$	-	$47 x$
					-	$14 x^{2}$	-	$7 x$

Step 9

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

				$3 x^{2}$	-	$7 x$
$2 x$	+	$1$		$6 x^{3}$	-	$11 x^{2}$	-	$47 x$	-	$20$
			-	$6 x^{3}$	-	$3 x^{2}$
					-	$14 x^{2}$	-	$47 x$
					+	$14 x^{2}$	+	$7 x$

Step 10

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

				$3 x^{2}$	-	$7 x$
$2 x$	+	$1$		$6 x^{3}$	-	$11 x^{2}$	-	$47 x$	-	$20$
			-	$6 x^{3}$	-	$3 x^{2}$
					-	$14 x^{2}$	-	$47 x$
					+	$14 x^{2}$	+	$7 x$
							-	$40 x$

Step 11

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

				$3 x^{2}$	-	$7 x$
$2 x$	+	$1$		$6 x^{3}$	-	$11 x^{2}$	-	$47 x$	-	$20$
			-	$6 x^{3}$	-	$3 x^{2}$
					-	$14 x^{2}$	-	$47 x$
					+	$14 x^{2}$	+	$7 x$
							-	$40 x$	-	$20$

Step 12

Divide the highest order term in the dividend $- 40 x$ by the highest order term in divisor $2 x$ .

				$3 x^{2}$	-	$7 x$	-	$20$
$2 x$	+	$1$		$6 x^{3}$	-	$11 x^{2}$	-	$47 x$	-	$20$
			-	$6 x^{3}$	-	$3 x^{2}$
					-	$14 x^{2}$	-	$47 x$
					+	$14 x^{2}$	+	$7 x$
							-	$40 x$	-	$20$

Step 13

Multiply the new quotient term by the divisor.

				$3 x^{2}$	-	$7 x$	-	$20$
$2 x$	+	$1$		$6 x^{3}$	-	$11 x^{2}$	-	$47 x$	-	$20$
			-	$6 x^{3}$	-	$3 x^{2}$
					-	$14 x^{2}$	-	$47 x$
					+	$14 x^{2}$	+	$7 x$
							-	$40 x$	-	$20$
							-	$40 x$	-	$20$

Step 14

The expression needs to be subtracted from the dividend, so change all the signs in $- 40 x - 20$

				$3 x^{2}$	-	$7 x$	-	$20$
$2 x$	+	$1$		$6 x^{3}$	-	$11 x^{2}$	-	$47 x$	-	$20$
			-	$6 x^{3}$	-	$3 x^{2}$
					-	$14 x^{2}$	-	$47 x$
					+	$14 x^{2}$	+	$7 x$
							-	$40 x$	-	$20$
							+	$40 x$	+	$20$

Step 15

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

				$3 x^{2}$	-	$7 x$	-	$20$
$2 x$	+	$1$		$6 x^{3}$	-	$11 x^{2}$	-	$47 x$	-	$20$
			-	$6 x^{3}$	-	$3 x^{2}$
					-	$14 x^{2}$	-	$47 x$
					+	$14 x^{2}$	+	$7 x$
							-	$40 x$	-	$20$
							+	$40 x$	+	$20$
										$0$

Step 16

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

$3 x^{2} - 7 x - 20$

Divide Using Long Polynomial Division (6x^3-11x^2-47x-20)÷(2x+1)

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