Divide Using Long Polynomial Division (11x^2+2x^3+14+17x)÷(2x+5)

$(11 x^{2} + 2 x^{3} + 14 + 17 x) \div (2 x + 5)$

Step 1

Expand $11 x^{2} + 2 x^{3} + 14 + 17 x$ .

Reorder $11 x^{2}$ and $2 x^{3}$ .

$\frac{2 x^{3} + 11 x^{2} + 14 + 17 x}{2 x + 5}$

Move $14$ .

$\frac{2 x^{3} + 11 x^{2} + 17 x + 14}{2 x + 5}$

Step 2

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

$2 x$

$5$

$2 x^{3}$

$11 x^{2}$

$17 x$

$14$

Step 3

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

					$x^{2}$
	$2 x$	+	$5$		$2 x^{3}$	+	$11 x^{2}$	+	$17 x$	+	$14$

Step 4

Multiply the new quotient term by the divisor.

				$x^{2}$
$2 x$	+	$5$		$2 x^{3}$	+	$11 x^{2}$	+	$17 x$	+	$14$
			+	$2 x^{3}$	+	$5 x^{2}$

Step 5

The expression needs to be subtracted from the dividend, so change all the signs in $2 x^{3} + 5 x^{2}$

				$x^{2}$
$2 x$	+	$5$		$2 x^{3}$	+	$11 x^{2}$	+	$17 x$	+	$14$
			-	$2 x^{3}$	-	$5 x^{2}$

Step 6

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

				$x^{2}$
$2 x$	+	$5$		$2 x^{3}$	+	$11 x^{2}$	+	$17 x$	+	$14$
			-	$2 x^{3}$	-	$5 x^{2}$
					+	$6 x^{2}$

Step 7

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

				$x^{2}$
$2 x$	+	$5$		$2 x^{3}$	+	$11 x^{2}$	+	$17 x$	+	$14$
			-	$2 x^{3}$	-	$5 x^{2}$
					+	$6 x^{2}$	+	$17 x$

Step 8

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

				$x^{2}$	+	$3 x$
$2 x$	+	$5$		$2 x^{3}$	+	$11 x^{2}$	+	$17 x$	+	$14$
			-	$2 x^{3}$	-	$5 x^{2}$
					+	$6 x^{2}$	+	$17 x$

Step 9

Multiply the new quotient term by the divisor.

				$x^{2}$	+	$3 x$
$2 x$	+	$5$		$2 x^{3}$	+	$11 x^{2}$	+	$17 x$	+	$14$
			-	$2 x^{3}$	-	$5 x^{2}$
					+	$6 x^{2}$	+	$17 x$
					+	$6 x^{2}$	+	$15 x$

Step 10

The expression needs to be subtracted from the dividend, so change all the signs in $6 x^{2} + 15 x$

				$x^{2}$	+	$3 x$
$2 x$	+	$5$		$2 x^{3}$	+	$11 x^{2}$	+	$17 x$	+	$14$
			-	$2 x^{3}$	-	$5 x^{2}$
					+	$6 x^{2}$	+	$17 x$
					-	$6 x^{2}$	-	$15 x$

Step 11

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

				$x^{2}$	+	$3 x$
$2 x$	+	$5$		$2 x^{3}$	+	$11 x^{2}$	+	$17 x$	+	$14$
			-	$2 x^{3}$	-	$5 x^{2}$
					+	$6 x^{2}$	+	$17 x$
					-	$6 x^{2}$	-	$15 x$
							+	$2 x$

Step 12

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

				$x^{2}$	+	$3 x$
$2 x$	+	$5$		$2 x^{3}$	+	$11 x^{2}$	+	$17 x$	+	$14$
			-	$2 x^{3}$	-	$5 x^{2}$
					+	$6 x^{2}$	+	$17 x$
					-	$6 x^{2}$	-	$15 x$
							+	$2 x$	+	$14$

Step 13

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

				$x^{2}$	+	$3 x$	+	$1$
$2 x$	+	$5$		$2 x^{3}$	+	$11 x^{2}$	+	$17 x$	+	$14$
			-	$2 x^{3}$	-	$5 x^{2}$
					+	$6 x^{2}$	+	$17 x$
					-	$6 x^{2}$	-	$15 x$
							+	$2 x$	+	$14$

Step 14

Multiply the new quotient term by the divisor.

				$x^{2}$	+	$3 x$	+	$1$
$2 x$	+	$5$		$2 x^{3}$	+	$11 x^{2}$	+	$17 x$	+	$14$
			-	$2 x^{3}$	-	$5 x^{2}$
					+	$6 x^{2}$	+	$17 x$
					-	$6 x^{2}$	-	$15 x$
							+	$2 x$	+	$14$
							+	$2 x$	+	$5$

Step 15

The expression needs to be subtracted from the dividend, so change all the signs in $2 x + 5$

				$x^{2}$	+	$3 x$	+	$1$
$2 x$	+	$5$		$2 x^{3}$	+	$11 x^{2}$	+	$17 x$	+	$14$
			-	$2 x^{3}$	-	$5 x^{2}$
					+	$6 x^{2}$	+	$17 x$
					-	$6 x^{2}$	-	$15 x$
							+	$2 x$	+	$14$
							-	$2 x$	-	$5$

Step 16

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

				$x^{2}$	+	$3 x$	+	$1$
$2 x$	+	$5$		$2 x^{3}$	+	$11 x^{2}$	+	$17 x$	+	$14$
			-	$2 x^{3}$	-	$5 x^{2}$
					+	$6 x^{2}$	+	$17 x$
					-	$6 x^{2}$	-	$15 x$
							+	$2 x$	+	$14$
							-	$2 x$	-	$5$
									+	$9$

Step 17

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

$x^{2} + 3 x + 1 + \frac{9}{2 x + 5}$

Divide Using Long Polynomial Division (11x^2+2x^3+14+17x)÷(2x+5)

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