Pre-Algebra Examples

$(2 x^{3} + 41 + 4 x^{2} + 12 x) \div (x + 3)$

Step 1

Expand $2 x^{3} + 41 + 4 x^{2} + 12 x$ .

Tap for more steps...

Step 1.1

Move $41$ .

$\frac{2 x^{3} + 4 x^{2} + 41 + 12 x}{x + 3}$

Step 1.2

Move $41$ .

$\frac{2 x^{3} + 4 x^{2} + 12 x + 41}{x + 3}$

Step 2

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

$x$

$3$

$2 x^{3}$

$4 x^{2}$

$12 x$

$41$

Step 3

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

					$2 x^{2}$
	$x$	+	$3$		$2 x^{3}$	+	$4 x^{2}$	+	$12 x$	+	$41$

Step 4

Multiply the new quotient term by the divisor.

				$2 x^{2}$
$x$	+	$3$		$2 x^{3}$	+	$4 x^{2}$	+	$12 x$	+	$41$
			+	$2 x^{3}$	+	$6 x^{2}$

Step 5

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

				$2 x^{2}$
$x$	+	$3$		$2 x^{3}$	+	$4 x^{2}$	+	$12 x$	+	$41$
			-	$2 x^{3}$	-	$6 x^{2}$

Step 6

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

				$2 x^{2}$
$x$	+	$3$		$2 x^{3}$	+	$4 x^{2}$	+	$12 x$	+	$41$
			-	$2 x^{3}$	-	$6 x^{2}$
					-	$2 x^{2}$

Step 7

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

				$2 x^{2}$
$x$	+	$3$		$2 x^{3}$	+	$4 x^{2}$	+	$12 x$	+	$41$
			-	$2 x^{3}$	-	$6 x^{2}$
					-	$2 x^{2}$	+	$12 x$

Step 8

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

				$2 x^{2}$	-	$2 x$
$x$	+	$3$		$2 x^{3}$	+	$4 x^{2}$	+	$12 x$	+	$41$
			-	$2 x^{3}$	-	$6 x^{2}$
					-	$2 x^{2}$	+	$12 x$

Step 9

Multiply the new quotient term by the divisor.

				$2 x^{2}$	-	$2 x$
$x$	+	$3$		$2 x^{3}$	+	$4 x^{2}$	+	$12 x$	+	$41$
			-	$2 x^{3}$	-	$6 x^{2}$
					-	$2 x^{2}$	+	$12 x$
					-	$2 x^{2}$	-	$6 x$

Step 10

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

				$2 x^{2}$	-	$2 x$
$x$	+	$3$		$2 x^{3}$	+	$4 x^{2}$	+	$12 x$	+	$41$
			-	$2 x^{3}$	-	$6 x^{2}$
					-	$2 x^{2}$	+	$12 x$
					+	$2 x^{2}$	+	$6 x$

Step 11

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

				$2 x^{2}$	-	$2 x$
$x$	+	$3$		$2 x^{3}$	+	$4 x^{2}$	+	$12 x$	+	$41$
			-	$2 x^{3}$	-	$6 x^{2}$
					-	$2 x^{2}$	+	$12 x$
					+	$2 x^{2}$	+	$6 x$
							+	$18 x$

Step 12

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

				$2 x^{2}$	-	$2 x$
$x$	+	$3$		$2 x^{3}$	+	$4 x^{2}$	+	$12 x$	+	$41$
			-	$2 x^{3}$	-	$6 x^{2}$
					-	$2 x^{2}$	+	$12 x$
					+	$2 x^{2}$	+	$6 x$
							+	$18 x$	+	$41$

Step 13

Divide the highest order term in the dividend $18 x$ by the highest order term in divisor $x$ .

				$2 x^{2}$	-	$2 x$	+	$18$
$x$	+	$3$		$2 x^{3}$	+	$4 x^{2}$	+	$12 x$	+	$41$
			-	$2 x^{3}$	-	$6 x^{2}$
					-	$2 x^{2}$	+	$12 x$
					+	$2 x^{2}$	+	$6 x$
							+	$18 x$	+	$41$

Step 14

Multiply the new quotient term by the divisor.

				$2 x^{2}$	-	$2 x$	+	$18$
$x$	+	$3$		$2 x^{3}$	+	$4 x^{2}$	+	$12 x$	+	$41$
			-	$2 x^{3}$	-	$6 x^{2}$
					-	$2 x^{2}$	+	$12 x$
					+	$2 x^{2}$	+	$6 x$
							+	$18 x$	+	$41$
							+	$18 x$	+	$54$

Step 15

The expression needs to be subtracted from the dividend, so change all the signs in $18 x + 54$

				$2 x^{2}$	-	$2 x$	+	$18$
$x$	+	$3$		$2 x^{3}$	+	$4 x^{2}$	+	$12 x$	+	$41$
			-	$2 x^{3}$	-	$6 x^{2}$
					-	$2 x^{2}$	+	$12 x$
					+	$2 x^{2}$	+	$6 x$
							+	$18 x$	+	$41$
							-	$18 x$	-	$54$

Step 16

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

				$2 x^{2}$	-	$2 x$	+	$18$
$x$	+	$3$		$2 x^{3}$	+	$4 x^{2}$	+	$12 x$	+	$41$
			-	$2 x^{3}$	-	$6 x^{2}$
					-	$2 x^{2}$	+	$12 x$
					+	$2 x^{2}$	+	$6 x$
							+	$18 x$	+	$41$
							-	$18 x$	-	$54$
									-	$13$

Step 17

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

$2 x^{2} - 2 x + 18 - \frac{13}{x + 3}$