Divide Using Long Polynomial Division (6x^3+14^2+6x-2)÷(2x+2)

$(6 x^{3} + 14^{2} + 6 x - 2) \div (2 x + 2)$

Step 1

Expand $6 x^{3} + 14^{2} + 6 x - 2$ .

Rewrite the exponentiation as a product.

$\frac{6 x^{3} + 14 \cdot 14 + 6 x - 2}{2 x + 2}$

Multiply $14$ by $14$ .

$\frac{6 x^{3} + 196 + 6 x - 2}{2 x + 2}$

Move $196$ .

$\frac{6 x^{3} + 6 x + 196 - 2}{2 x + 2}$

Subtract $2$ from $196$ .

$\frac{6 x^{3} + 6 x + 194}{2 x + 2}$

Step 2

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

$2 x$

$2$

$6 x^{3}$

$0 x^{2}$

$6 x$

$194$

Step 3

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

					$3 x^{2}$
	$2 x$	+	$2$		$6 x^{3}$	+	$0 x^{2}$	+	$6 x$	+	$194$

Step 4

Multiply the new quotient term by the divisor.

				$3 x^{2}$
$2 x$	+	$2$		$6 x^{3}$	+	$0 x^{2}$	+	$6 x$	+	$194$
			+	$6 x^{3}$	+	$6 x^{2}$

Step 5

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

				$3 x^{2}$
$2 x$	+	$2$		$6 x^{3}$	+	$0 x^{2}$	+	$6 x$	+	$194$
			-	$6 x^{3}$	-	$6 x^{2}$

Step 6

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

				$3 x^{2}$
$2 x$	+	$2$		$6 x^{3}$	+	$0 x^{2}$	+	$6 x$	+	$194$
			-	$6 x^{3}$	-	$6 x^{2}$
					-	$6 x^{2}$

Step 7

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

				$3 x^{2}$
$2 x$	+	$2$		$6 x^{3}$	+	$0 x^{2}$	+	$6 x$	+	$194$
			-	$6 x^{3}$	-	$6 x^{2}$
					-	$6 x^{2}$	+	$6 x$

Step 8

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

				$3 x^{2}$	-	$3 x$
$2 x$	+	$2$		$6 x^{3}$	+	$0 x^{2}$	+	$6 x$	+	$194$
			-	$6 x^{3}$	-	$6 x^{2}$
					-	$6 x^{2}$	+	$6 x$

Step 9

Multiply the new quotient term by the divisor.

				$3 x^{2}$	-	$3 x$
$2 x$	+	$2$		$6 x^{3}$	+	$0 x^{2}$	+	$6 x$	+	$194$
			-	$6 x^{3}$	-	$6 x^{2}$
					-	$6 x^{2}$	+	$6 x$
					-	$6 x^{2}$	-	$6 x$

Step 10

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

				$3 x^{2}$	-	$3 x$
$2 x$	+	$2$		$6 x^{3}$	+	$0 x^{2}$	+	$6 x$	+	$194$
			-	$6 x^{3}$	-	$6 x^{2}$
					-	$6 x^{2}$	+	$6 x$
					+	$6 x^{2}$	+	$6 x$

Step 11

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

				$3 x^{2}$	-	$3 x$
$2 x$	+	$2$		$6 x^{3}$	+	$0 x^{2}$	+	$6 x$	+	$194$
			-	$6 x^{3}$	-	$6 x^{2}$
					-	$6 x^{2}$	+	$6 x$
					+	$6 x^{2}$	+	$6 x$
							+	$12 x$

Step 12

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

				$3 x^{2}$	-	$3 x$
$2 x$	+	$2$		$6 x^{3}$	+	$0 x^{2}$	+	$6 x$	+	$194$
			-	$6 x^{3}$	-	$6 x^{2}$
					-	$6 x^{2}$	+	$6 x$
					+	$6 x^{2}$	+	$6 x$
							+	$12 x$	+	$194$

Step 13

Divide the highest order term in the dividend $12 x$ by the highest order term in divisor $2 x$ .

				$3 x^{2}$	-	$3 x$	+	$6$
$2 x$	+	$2$		$6 x^{3}$	+	$0 x^{2}$	+	$6 x$	+	$194$
			-	$6 x^{3}$	-	$6 x^{2}$
					-	$6 x^{2}$	+	$6 x$
					+	$6 x^{2}$	+	$6 x$
							+	$12 x$	+	$194$

Step 14

Multiply the new quotient term by the divisor.

				$3 x^{2}$	-	$3 x$	+	$6$
$2 x$	+	$2$		$6 x^{3}$	+	$0 x^{2}$	+	$6 x$	+	$194$
			-	$6 x^{3}$	-	$6 x^{2}$
					-	$6 x^{2}$	+	$6 x$
					+	$6 x^{2}$	+	$6 x$
							+	$12 x$	+	$194$
							+	$12 x$	+	$12$

Step 15

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

				$3 x^{2}$	-	$3 x$	+	$6$
$2 x$	+	$2$		$6 x^{3}$	+	$0 x^{2}$	+	$6 x$	+	$194$
			-	$6 x^{3}$	-	$6 x^{2}$
					-	$6 x^{2}$	+	$6 x$
					+	$6 x^{2}$	+	$6 x$
							+	$12 x$	+	$194$
							-	$12 x$	-	$12$

Step 16

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

				$3 x^{2}$	-	$3 x$	+	$6$
$2 x$	+	$2$		$6 x^{3}$	+	$0 x^{2}$	+	$6 x$	+	$194$
			-	$6 x^{3}$	-	$6 x^{2}$
					-	$6 x^{2}$	+	$6 x$
					+	$6 x^{2}$	+	$6 x$
							+	$12 x$	+	$194$
							-	$12 x$	-	$12$
									+	$182$

Step 17

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

$3 x^{2} - 3 x + 6 + \frac{182}{2 x + 2}$

Divide Using Long Polynomial Division (6x^3+14^2+6x-2)÷(2x+2)

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