Divide Using Long Polynomial Division (12x^3+2+11x+20x^2)÷(2x+1)

$(12 x^{3} + 2 + 11 x + 20 x^{2}) \div (2 x + 1)$

Step 1

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

Move $2$ .

$\frac{12 x^{3} + 11 x + 2 + 20 x^{2}}{2 x + 1}$

Move $2$ .

$\frac{12 x^{3} + 11 x + 20 x^{2} + 2}{2 x + 1}$

Move $11 x$ .

$\frac{12 x^{3} + 20 x^{2} + 11 x + 2}{2 x + 1}$

Step 2

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

$2 x$

$1$

$12 x^{3}$

$20 x^{2}$

$11 x$

$2$

Step 3

Divide the highest order term in the dividend $12 x^{3}$ by the highest order term in divisor $2 x$ .

					$6 x^{2}$
	$2 x$	+	$1$		$12 x^{3}$	+	$20 x^{2}$	+	$11 x$	+	$2$

Step 4

Multiply the new quotient term by the divisor.

				$6 x^{2}$
$2 x$	+	$1$		$12 x^{3}$	+	$20 x^{2}$	+	$11 x$	+	$2$
			+	$12 x^{3}$	+	$6 x^{2}$

Step 5

The expression needs to be subtracted from the dividend, so change all the signs in $12 x^{3} + 6 x^{2}$

				$6 x^{2}$
$2 x$	+	$1$		$12 x^{3}$	+	$20 x^{2}$	+	$11 x$	+	$2$
			-	$12 x^{3}$	-	$6 x^{2}$

Step 6

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

				$6 x^{2}$
$2 x$	+	$1$		$12 x^{3}$	+	$20 x^{2}$	+	$11 x$	+	$2$
			-	$12 x^{3}$	-	$6 x^{2}$
					+	$14 x^{2}$

Step 7

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

				$6 x^{2}$
$2 x$	+	$1$		$12 x^{3}$	+	$20 x^{2}$	+	$11 x$	+	$2$
			-	$12 x^{3}$	-	$6 x^{2}$
					+	$14 x^{2}$	+	$11 x$

Step 8

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

				$6 x^{2}$	+	$7 x$
$2 x$	+	$1$		$12 x^{3}$	+	$20 x^{2}$	+	$11 x$	+	$2$
			-	$12 x^{3}$	-	$6 x^{2}$
					+	$14 x^{2}$	+	$11 x$

Step 9

Multiply the new quotient term by the divisor.

				$6 x^{2}$	+	$7 x$
$2 x$	+	$1$		$12 x^{3}$	+	$20 x^{2}$	+	$11 x$	+	$2$
			-	$12 x^{3}$	-	$6 x^{2}$
					+	$14 x^{2}$	+	$11 x$
					+	$14 x^{2}$	+	$7 x$

Step 10

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

				$6 x^{2}$	+	$7 x$
$2 x$	+	$1$		$12 x^{3}$	+	$20 x^{2}$	+	$11 x$	+	$2$
			-	$12 x^{3}$	-	$6 x^{2}$
					+	$14 x^{2}$	+	$11 x$
					-	$14 x^{2}$	-	$7 x$

Step 11

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

				$6 x^{2}$	+	$7 x$
$2 x$	+	$1$		$12 x^{3}$	+	$20 x^{2}$	+	$11 x$	+	$2$
			-	$12 x^{3}$	-	$6 x^{2}$
					+	$14 x^{2}$	+	$11 x$
					-	$14 x^{2}$	-	$7 x$
							+	$4 x$

Step 12

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

				$6 x^{2}$	+	$7 x$
$2 x$	+	$1$		$12 x^{3}$	+	$20 x^{2}$	+	$11 x$	+	$2$
			-	$12 x^{3}$	-	$6 x^{2}$
					+	$14 x^{2}$	+	$11 x$
					-	$14 x^{2}$	-	$7 x$
							+	$4 x$	+	$2$

Step 13

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

				$6 x^{2}$	+	$7 x$	+	$2$
$2 x$	+	$1$		$12 x^{3}$	+	$20 x^{2}$	+	$11 x$	+	$2$
			-	$12 x^{3}$	-	$6 x^{2}$
					+	$14 x^{2}$	+	$11 x$
					-	$14 x^{2}$	-	$7 x$
							+	$4 x$	+	$2$

Step 14

Multiply the new quotient term by the divisor.

				$6 x^{2}$	+	$7 x$	+	$2$
$2 x$	+	$1$		$12 x^{3}$	+	$20 x^{2}$	+	$11 x$	+	$2$
			-	$12 x^{3}$	-	$6 x^{2}$
					+	$14 x^{2}$	+	$11 x$
					-	$14 x^{2}$	-	$7 x$
							+	$4 x$	+	$2$
							+	$4 x$	+	$2$

Step 15

The expression needs to be subtracted from the dividend, so change all the signs in $4 x + 2$

				$6 x^{2}$	+	$7 x$	+	$2$
$2 x$	+	$1$		$12 x^{3}$	+	$20 x^{2}$	+	$11 x$	+	$2$
			-	$12 x^{3}$	-	$6 x^{2}$
					+	$14 x^{2}$	+	$11 x$
					-	$14 x^{2}$	-	$7 x$
							+	$4 x$	+	$2$
							-	$4 x$	-	$2$

Step 16

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

				$6 x^{2}$	+	$7 x$	+	$2$
$2 x$	+	$1$		$12 x^{3}$	+	$20 x^{2}$	+	$11 x$	+	$2$
			-	$12 x^{3}$	-	$6 x^{2}$
					+	$14 x^{2}$	+	$11 x$
					-	$14 x^{2}$	-	$7 x$
							+	$4 x$	+	$2$
							-	$4 x$	-	$2$
										$0$

Step 17

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

$6 x^{2} + 7 x + 2$

Divide Using Long Polynomial Division (12x^3+2+11x+20x^2)÷(2x+1)

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