Pre-Algebra Examples

$x^{3} - 5 x^{2} + 3 x - 15$ , $x + 3$

Step 1

Divide the first expression by the second expression.

$\frac{x^{3} - 5 x^{2} + 3 x - 15}{x + 3}$

Step 2

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

$x$

$3$

$x^{3}$

$5 x^{2}$

$3 x$

$15$

Step 3

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

					$x^{2}$
	$x$	+	$3$		$x^{3}$	-	$5 x^{2}$	+	$3 x$	-	$15$

Step 4

Multiply the new quotient term by the divisor.

				$x^{2}$
$x$	+	$3$		$x^{3}$	-	$5 x^{2}$	+	$3 x$	-	$15$
			+	$x^{3}$	+	$3 x^{2}$

Step 5

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

				$x^{2}$
$x$	+	$3$		$x^{3}$	-	$5 x^{2}$	+	$3 x$	-	$15$
			-	$x^{3}$	-	$3 x^{2}$

Step 6

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

				$x^{2}$
$x$	+	$3$		$x^{3}$	-	$5 x^{2}$	+	$3 x$	-	$15$
			-	$x^{3}$	-	$3 x^{2}$
					-	$8 x^{2}$

Step 7

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

				$x^{2}$
$x$	+	$3$		$x^{3}$	-	$5 x^{2}$	+	$3 x$	-	$15$
			-	$x^{3}$	-	$3 x^{2}$
					-	$8 x^{2}$	+	$3 x$

Step 8

Divide the highest order term in the dividend $- 8 x^{2}$ by the highest order term in divisor $x$ .

				$x^{2}$	-	$8 x$
$x$	+	$3$		$x^{3}$	-	$5 x^{2}$	+	$3 x$	-	$15$
			-	$x^{3}$	-	$3 x^{2}$
					-	$8 x^{2}$	+	$3 x$

Step 9

Multiply the new quotient term by the divisor.

				$x^{2}$	-	$8 x$
$x$	+	$3$		$x^{3}$	-	$5 x^{2}$	+	$3 x$	-	$15$
			-	$x^{3}$	-	$3 x^{2}$
					-	$8 x^{2}$	+	$3 x$
					-	$8 x^{2}$	-	$24 x$

Step 10

The expression needs to be subtracted from the dividend, so change all the signs in $- 8 x^{2} - 24 x$

				$x^{2}$	-	$8 x$
$x$	+	$3$		$x^{3}$	-	$5 x^{2}$	+	$3 x$	-	$15$
			-	$x^{3}$	-	$3 x^{2}$
					-	$8 x^{2}$	+	$3 x$
					+	$8 x^{2}$	+	$24 x$

Step 11

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

				$x^{2}$	-	$8 x$
$x$	+	$3$		$x^{3}$	-	$5 x^{2}$	+	$3 x$	-	$15$
			-	$x^{3}$	-	$3 x^{2}$
					-	$8 x^{2}$	+	$3 x$
					+	$8 x^{2}$	+	$24 x$
							+	$27 x$

Step 12

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

				$x^{2}$	-	$8 x$
$x$	+	$3$		$x^{3}$	-	$5 x^{2}$	+	$3 x$	-	$15$
			-	$x^{3}$	-	$3 x^{2}$
					-	$8 x^{2}$	+	$3 x$
					+	$8 x^{2}$	+	$24 x$
							+	$27 x$	-	$15$

Step 13

Divide the highest order term in the dividend $27 x$ by the highest order term in divisor $x$ .

				$x^{2}$	-	$8 x$	+	$27$
$x$	+	$3$		$x^{3}$	-	$5 x^{2}$	+	$3 x$	-	$15$
			-	$x^{3}$	-	$3 x^{2}$
					-	$8 x^{2}$	+	$3 x$
					+	$8 x^{2}$	+	$24 x$
							+	$27 x$	-	$15$

Step 14

Multiply the new quotient term by the divisor.

				$x^{2}$	-	$8 x$	+	$27$
$x$	+	$3$		$x^{3}$	-	$5 x^{2}$	+	$3 x$	-	$15$
			-	$x^{3}$	-	$3 x^{2}$
					-	$8 x^{2}$	+	$3 x$
					+	$8 x^{2}$	+	$24 x$
							+	$27 x$	-	$15$
							+	$27 x$	+	$81$

Step 15

The expression needs to be subtracted from the dividend, so change all the signs in $27 x + 81$

				$x^{2}$	-	$8 x$	+	$27$
$x$	+	$3$		$x^{3}$	-	$5 x^{2}$	+	$3 x$	-	$15$
			-	$x^{3}$	-	$3 x^{2}$
					-	$8 x^{2}$	+	$3 x$
					+	$8 x^{2}$	+	$24 x$
							+	$27 x$	-	$15$
							-	$27 x$	-	$81$

Step 16

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

				$x^{2}$	-	$8 x$	+	$27$
$x$	+	$3$		$x^{3}$	-	$5 x^{2}$	+	$3 x$	-	$15$
			-	$x^{3}$	-	$3 x^{2}$
					-	$8 x^{2}$	+	$3 x$
					+	$8 x^{2}$	+	$24 x$
							+	$27 x$	-	$15$
							-	$27 x$	-	$81$
									-	$96$

Step 17

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

$x^{2} - 8 x + 27 - \frac{96}{x + 3}$

Enter YOUR Problem