Pre-Algebra Examples

$x^{3} + 4$ , $x - 5$

Step 1

Divide the first expression by the second expression.

$\frac{x^{3} + 4}{x - 5}$

Step 2

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

$x$

$5$

$x^{3}$

$0 x^{2}$

$0 x$

$4$

Step 3

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

					$x^{2}$
	$x$	-	$5$		$x^{3}$	+	$0 x^{2}$	+	$0 x$	+	$4$

Step 4

Multiply the new quotient term by the divisor.

				$x^{2}$
$x$	-	$5$		$x^{3}$	+	$0 x^{2}$	+	$0 x$	+	$4$
			+	$x^{3}$	-	$5 x^{2}$

Step 5

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

				$x^{2}$
$x$	-	$5$		$x^{3}$	+	$0 x^{2}$	+	$0 x$	+	$4$
			-	$x^{3}$	+	$5 x^{2}$

Step 6

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

				$x^{2}$
$x$	-	$5$		$x^{3}$	+	$0 x^{2}$	+	$0 x$	+	$4$
			-	$x^{3}$	+	$5 x^{2}$
					+	$5 x^{2}$

Step 7

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

				$x^{2}$
$x$	-	$5$		$x^{3}$	+	$0 x^{2}$	+	$0 x$	+	$4$
			-	$x^{3}$	+	$5 x^{2}$
					+	$5 x^{2}$	+	$0 x$

Step 8

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

				$x^{2}$	+	$5 x$
$x$	-	$5$		$x^{3}$	+	$0 x^{2}$	+	$0 x$	+	$4$
			-	$x^{3}$	+	$5 x^{2}$
					+	$5 x^{2}$	+	$0 x$

Step 9

Multiply the new quotient term by the divisor.

				$x^{2}$	+	$5 x$
$x$	-	$5$		$x^{3}$	+	$0 x^{2}$	+	$0 x$	+	$4$
			-	$x^{3}$	+	$5 x^{2}$
					+	$5 x^{2}$	+	$0 x$
					+	$5 x^{2}$	-	$25 x$

Step 10

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

				$x^{2}$	+	$5 x$
$x$	-	$5$		$x^{3}$	+	$0 x^{2}$	+	$0 x$	+	$4$
			-	$x^{3}$	+	$5 x^{2}$
					+	$5 x^{2}$	+	$0 x$
					-	$5 x^{2}$	+	$25 x$

Step 11

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

				$x^{2}$	+	$5 x$
$x$	-	$5$		$x^{3}$	+	$0 x^{2}$	+	$0 x$	+	$4$
			-	$x^{3}$	+	$5 x^{2}$
					+	$5 x^{2}$	+	$0 x$
					-	$5 x^{2}$	+	$25 x$
							+	$25 x$

Step 12

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

				$x^{2}$	+	$5 x$
$x$	-	$5$		$x^{3}$	+	$0 x^{2}$	+	$0 x$	+	$4$
			-	$x^{3}$	+	$5 x^{2}$
					+	$5 x^{2}$	+	$0 x$
					-	$5 x^{2}$	+	$25 x$
							+	$25 x$	+	$4$

Step 13

Divide the highest order term in the dividend $25 x$ by the highest order term in divisor $x$ .

				$x^{2}$	+	$5 x$	+	$25$
$x$	-	$5$		$x^{3}$	+	$0 x^{2}$	+	$0 x$	+	$4$
			-	$x^{3}$	+	$5 x^{2}$
					+	$5 x^{2}$	+	$0 x$
					-	$5 x^{2}$	+	$25 x$
							+	$25 x$	+	$4$

Step 14

Multiply the new quotient term by the divisor.

				$x^{2}$	+	$5 x$	+	$25$
$x$	-	$5$		$x^{3}$	+	$0 x^{2}$	+	$0 x$	+	$4$
			-	$x^{3}$	+	$5 x^{2}$
					+	$5 x^{2}$	+	$0 x$
					-	$5 x^{2}$	+	$25 x$
							+	$25 x$	+	$4$
							+	$25 x$	-	$125$

Step 15

The expression needs to be subtracted from the dividend, so change all the signs in $25 x - 125$

				$x^{2}$	+	$5 x$	+	$25$
$x$	-	$5$		$x^{3}$	+	$0 x^{2}$	+	$0 x$	+	$4$
			-	$x^{3}$	+	$5 x^{2}$
					+	$5 x^{2}$	+	$0 x$
					-	$5 x^{2}$	+	$25 x$
							+	$25 x$	+	$4$
							-	$25 x$	+	$125$

Step 16

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

				$x^{2}$	+	$5 x$	+	$25$
$x$	-	$5$		$x^{3}$	+	$0 x^{2}$	+	$0 x$	+	$4$
			-	$x^{3}$	+	$5 x^{2}$
					+	$5 x^{2}$	+	$0 x$
					-	$5 x^{2}$	+	$25 x$
							+	$25 x$	+	$4$
							-	$25 x$	+	$125$
									+	$129$

Step 17

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

$x^{2} + 5 x + 25 + \frac{129}{x - 5}$

Enter YOUR Problem