Pre-Algebra Examples

$\frac{5 m^{3} + 25 m^{2} - 23 + 42}{m + 6}$

Step 1

Add $- 23$ and $42$ .

$\frac{5 m^{3} + 25 m^{2} + 19}{m + 6}$

Step 2

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

$m$

$6$

$5 m^{3}$

$25 m^{2}$

$0 m$

$19$

Step 3

Divide the highest order term in the dividend $5 m^{3}$ by the highest order term in divisor $m$ .

					$5 m^{2}$
	$m$	+	$6$		$5 m^{3}$	+	$25 m^{2}$	+	$0 m$	+	$19$

Step 4

Multiply the new quotient term by the divisor.

				$5 m^{2}$
$m$	+	$6$		$5 m^{3}$	+	$25 m^{2}$	+	$0 m$	+	$19$
			+	$5 m^{3}$	+	$30 m^{2}$

Step 5

The expression needs to be subtracted from the dividend, so change all the signs in $5 m^{3} + 30 m^{2}$

				$5 m^{2}$
$m$	+	$6$		$5 m^{3}$	+	$25 m^{2}$	+	$0 m$	+	$19$
			-	$5 m^{3}$	-	$30 m^{2}$

Step 6

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

				$5 m^{2}$
$m$	+	$6$		$5 m^{3}$	+	$25 m^{2}$	+	$0 m$	+	$19$
			-	$5 m^{3}$	-	$30 m^{2}$
					-	$5 m^{2}$

Step 7

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

				$5 m^{2}$
$m$	+	$6$		$5 m^{3}$	+	$25 m^{2}$	+	$0 m$	+	$19$
			-	$5 m^{3}$	-	$30 m^{2}$
					-	$5 m^{2}$	+	$0 m$

Step 8

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

				$5 m^{2}$	-	$5 m$
$m$	+	$6$		$5 m^{3}$	+	$25 m^{2}$	+	$0 m$	+	$19$
			-	$5 m^{3}$	-	$30 m^{2}$
					-	$5 m^{2}$	+	$0 m$

Step 9

Multiply the new quotient term by the divisor.

				$5 m^{2}$	-	$5 m$
$m$	+	$6$		$5 m^{3}$	+	$25 m^{2}$	+	$0 m$	+	$19$
			-	$5 m^{3}$	-	$30 m^{2}$
					-	$5 m^{2}$	+	$0 m$
					-	$5 m^{2}$	-	$30 m$

Step 10

The expression needs to be subtracted from the dividend, so change all the signs in $- 5 m^{2} - 30 m$

				$5 m^{2}$	-	$5 m$
$m$	+	$6$		$5 m^{3}$	+	$25 m^{2}$	+	$0 m$	+	$19$
			-	$5 m^{3}$	-	$30 m^{2}$
					-	$5 m^{2}$	+	$0 m$
					+	$5 m^{2}$	+	$30 m$

Step 11

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

				$5 m^{2}$	-	$5 m$
$m$	+	$6$		$5 m^{3}$	+	$25 m^{2}$	+	$0 m$	+	$19$
			-	$5 m^{3}$	-	$30 m^{2}$
					-	$5 m^{2}$	+	$0 m$
					+	$5 m^{2}$	+	$30 m$
							+	$30 m$

Step 12

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

				$5 m^{2}$	-	$5 m$
$m$	+	$6$		$5 m^{3}$	+	$25 m^{2}$	+	$0 m$	+	$19$
			-	$5 m^{3}$	-	$30 m^{2}$
					-	$5 m^{2}$	+	$0 m$
					+	$5 m^{2}$	+	$30 m$
							+	$30 m$	+	$19$

Step 13

Divide the highest order term in the dividend $30 m$ by the highest order term in divisor $m$ .

				$5 m^{2}$	-	$5 m$	+	$30$
$m$	+	$6$		$5 m^{3}$	+	$25 m^{2}$	+	$0 m$	+	$19$
			-	$5 m^{3}$	-	$30 m^{2}$
					-	$5 m^{2}$	+	$0 m$
					+	$5 m^{2}$	+	$30 m$
							+	$30 m$	+	$19$

Step 14

Multiply the new quotient term by the divisor.

				$5 m^{2}$	-	$5 m$	+	$30$
$m$	+	$6$		$5 m^{3}$	+	$25 m^{2}$	+	$0 m$	+	$19$
			-	$5 m^{3}$	-	$30 m^{2}$
					-	$5 m^{2}$	+	$0 m$
					+	$5 m^{2}$	+	$30 m$
							+	$30 m$	+	$19$
							+	$30 m$	+	$180$

Step 15

The expression needs to be subtracted from the dividend, so change all the signs in $30 m + 180$

				$5 m^{2}$	-	$5 m$	+	$30$
$m$	+	$6$		$5 m^{3}$	+	$25 m^{2}$	+	$0 m$	+	$19$
			-	$5 m^{3}$	-	$30 m^{2}$
					-	$5 m^{2}$	+	$0 m$
					+	$5 m^{2}$	+	$30 m$
							+	$30 m$	+	$19$
							-	$30 m$	-	$180$

Step 16

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

				$5 m^{2}$	-	$5 m$	+	$30$
$m$	+	$6$		$5 m^{3}$	+	$25 m^{2}$	+	$0 m$	+	$19$
			-	$5 m^{3}$	-	$30 m^{2}$
					-	$5 m^{2}$	+	$0 m$
					+	$5 m^{2}$	+	$30 m$
							+	$30 m$	+	$19$
							-	$30 m$	-	$180$
									-	$161$

Step 17

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

$5 m^{2} - 5 m + 30 - \frac{161}{m + 6}$