Pre-Algebra Examples

$(- 21 - 4 p + 3 p^{2}) \div (3 + p)$

Step 1

Expand $- 21 - 4 p + 3 p^{2}$ .

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Step 1.1

Reorder $- 21$ and $- 4 p$ .

$\frac{- 4 p - 21 + 3 p^{2}}{3 + p}$

Step 1.2

Move $- 21$ .

$\frac{- 4 p + 3 p^{2} - 21}{3 + p}$

Step 1.3

Reorder $- 4 p$ and $3 p^{2}$ .

$\frac{3 p^{2} - 4 p - 21}{3 + p}$

Step 2

Reorder $3$ and $p$ .

$\frac{3 p^{2} - 4 p - 21}{p + 3}$

Step 3

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

$p$

$3$

$3 p^{2}$

$4 p$

$21$

Step 4

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

					$3 p$
	$p$	+	$3$		$3 p^{2}$	-	$4 p$	-	$21$

Step 5

Multiply the new quotient term by the divisor.

				$3 p$
$p$	+	$3$		$3 p^{2}$	-	$4 p$	-	$21$
			+	$3 p^{2}$	+	$9 p$

Step 6

The expression needs to be subtracted from the dividend, so change all the signs in $3 p^{2} + 9 p$

				$3 p$
$p$	+	$3$		$3 p^{2}$	-	$4 p$	-	$21$
			-	$3 p^{2}$	-	$9 p$

Step 7

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

				$3 p$
$p$	+	$3$		$3 p^{2}$	-	$4 p$	-	$21$
			-	$3 p^{2}$	-	$9 p$
					-	$13 p$

Step 8

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

				$3 p$
$p$	+	$3$		$3 p^{2}$	-	$4 p$	-	$21$
			-	$3 p^{2}$	-	$9 p$
					-	$13 p$	-	$21$

Step 9

Divide the highest order term in the dividend $- 13 p$ by the highest order term in divisor $p$ .

				$3 p$	-	$13$
$p$	+	$3$		$3 p^{2}$	-	$4 p$	-	$21$
			-	$3 p^{2}$	-	$9 p$
					-	$13 p$	-	$21$

Step 10

Multiply the new quotient term by the divisor.

				$3 p$	-	$13$
$p$	+	$3$		$3 p^{2}$	-	$4 p$	-	$21$
			-	$3 p^{2}$	-	$9 p$
					-	$13 p$	-	$21$
					-	$13 p$	-	$39$

Step 11

The expression needs to be subtracted from the dividend, so change all the signs in $- 13 p - 39$

				$3 p$	-	$13$
$p$	+	$3$		$3 p^{2}$	-	$4 p$	-	$21$
			-	$3 p^{2}$	-	$9 p$
					-	$13 p$	-	$21$
					+	$13 p$	+	$39$

Step 12

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

				$3 p$	-	$13$
$p$	+	$3$		$3 p^{2}$	-	$4 p$	-	$21$
			-	$3 p^{2}$	-	$9 p$
					-	$13 p$	-	$21$
					+	$13 p$	+	$39$
							+	$18$

Step 13

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

$3 p - 13 + \frac{18}{p + 3}$