Divide Using Long Polynomial Division (2x^3-18x-45+5x^2)÷(x+5)

$(2 x^{3} - 18 x - 45 + 5 x^{2}) \div (x + 5)$

Step 1

Expand $2 x^{3} - 18 x - 45 + 5 x^{2}$ .

Move $- 45$ .

$\frac{2 x^{3} - 18 x + 5 x^{2} - 45}{x + 5}$

Move $- 18 x$ .

$\frac{2 x^{3} + 5 x^{2} - 18 x - 45}{x + 5}$

Step 2

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

$x$

$5$

$2 x^{3}$

$5 x^{2}$

$18 x$

$45$

Step 3

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

					$2 x^{2}$
	$x$	+	$5$		$2 x^{3}$	+	$5 x^{2}$	-	$18 x$	-	$45$

Step 4

Multiply the new quotient term by the divisor.

				$2 x^{2}$
$x$	+	$5$		$2 x^{3}$	+	$5 x^{2}$	-	$18 x$	-	$45$
			+	$2 x^{3}$	+	$10 x^{2}$

Step 5

The expression needs to be subtracted from the dividend, so change all the signs in $2 x^{3} + 10 x^{2}$

				$2 x^{2}$
$x$	+	$5$		$2 x^{3}$	+	$5 x^{2}$	-	$18 x$	-	$45$
			-	$2 x^{3}$	-	$10 x^{2}$

Step 6

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

				$2 x^{2}$
$x$	+	$5$		$2 x^{3}$	+	$5 x^{2}$	-	$18 x$	-	$45$
			-	$2 x^{3}$	-	$10 x^{2}$
					-	$5 x^{2}$

Step 7

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

				$2 x^{2}$
$x$	+	$5$		$2 x^{3}$	+	$5 x^{2}$	-	$18 x$	-	$45$
			-	$2 x^{3}$	-	$10 x^{2}$
					-	$5 x^{2}$	-	$18 x$

Step 8

Divide the highest order term in the dividend $- 5 x^{2}$ by the highest order term in divisor $x$ .

				$2 x^{2}$	-	$5 x$
$x$	+	$5$		$2 x^{3}$	+	$5 x^{2}$	-	$18 x$	-	$45$
			-	$2 x^{3}$	-	$10 x^{2}$
					-	$5 x^{2}$	-	$18 x$

Step 9

Multiply the new quotient term by the divisor.

				$2 x^{2}$	-	$5 x$
$x$	+	$5$		$2 x^{3}$	+	$5 x^{2}$	-	$18 x$	-	$45$
			-	$2 x^{3}$	-	$10 x^{2}$
					-	$5 x^{2}$	-	$18 x$
					-	$5 x^{2}$	-	$25 x$

Step 10

The expression needs to be subtracted from the dividend, so change all the signs in $- 5 x^{2} - 25 x$

				$2 x^{2}$	-	$5 x$
$x$	+	$5$		$2 x^{3}$	+	$5 x^{2}$	-	$18 x$	-	$45$
			-	$2 x^{3}$	-	$10 x^{2}$
					-	$5 x^{2}$	-	$18 x$
					+	$5 x^{2}$	+	$25 x$

Step 11

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

				$2 x^{2}$	-	$5 x$
$x$	+	$5$		$2 x^{3}$	+	$5 x^{2}$	-	$18 x$	-	$45$
			-	$2 x^{3}$	-	$10 x^{2}$
					-	$5 x^{2}$	-	$18 x$
					+	$5 x^{2}$	+	$25 x$
							+	$7 x$

Step 12

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

				$2 x^{2}$	-	$5 x$
$x$	+	$5$		$2 x^{3}$	+	$5 x^{2}$	-	$18 x$	-	$45$
			-	$2 x^{3}$	-	$10 x^{2}$
					-	$5 x^{2}$	-	$18 x$
					+	$5 x^{2}$	+	$25 x$
							+	$7 x$	-	$45$

Step 13

Divide the highest order term in the dividend $7 x$ by the highest order term in divisor $x$ .

				$2 x^{2}$	-	$5 x$	+	$7$
$x$	+	$5$		$2 x^{3}$	+	$5 x^{2}$	-	$18 x$	-	$45$
			-	$2 x^{3}$	-	$10 x^{2}$
					-	$5 x^{2}$	-	$18 x$
					+	$5 x^{2}$	+	$25 x$
							+	$7 x$	-	$45$

Step 14

Multiply the new quotient term by the divisor.

				$2 x^{2}$	-	$5 x$	+	$7$
$x$	+	$5$		$2 x^{3}$	+	$5 x^{2}$	-	$18 x$	-	$45$
			-	$2 x^{3}$	-	$10 x^{2}$
					-	$5 x^{2}$	-	$18 x$
					+	$5 x^{2}$	+	$25 x$
							+	$7 x$	-	$45$
							+	$7 x$	+	$35$

Step 15

The expression needs to be subtracted from the dividend, so change all the signs in $7 x + 35$

				$2 x^{2}$	-	$5 x$	+	$7$
$x$	+	$5$		$2 x^{3}$	+	$5 x^{2}$	-	$18 x$	-	$45$
			-	$2 x^{3}$	-	$10 x^{2}$
					-	$5 x^{2}$	-	$18 x$
					+	$5 x^{2}$	+	$25 x$
							+	$7 x$	-	$45$
							-	$7 x$	-	$35$

Step 16

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

				$2 x^{2}$	-	$5 x$	+	$7$
$x$	+	$5$		$2 x^{3}$	+	$5 x^{2}$	-	$18 x$	-	$45$
			-	$2 x^{3}$	-	$10 x^{2}$
					-	$5 x^{2}$	-	$18 x$
					+	$5 x^{2}$	+	$25 x$
							+	$7 x$	-	$45$
							-	$7 x$	-	$35$
									-	$80$

Step 17

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

$2 x^{2} - 5 x + 7 - \frac{80}{x + 5}$

Divide Using Long Polynomial Division (2x^3-18x-45+5x^2)÷(x+5)

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