Pre-Algebra Examples

$\frac{w^{2} + 8}{w^{2} - 5 w - 14}$

Step 1

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

$w^{2}$

$5 w$

$14$

$w^{2}$

$0 w$

$8$

Step 2

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

							$1$
	$w^{2}$	-	$5 w$	-	$14$		$w^{2}$	+	$0 w$	+	$8$

Step 3

Multiply the new quotient term by the divisor.

Step 4

The expression needs to be subtracted from the dividend, so change all the signs in $w^{2} - 5 w - 14$

Step 5

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

Step 6

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

$1 + \frac{5 w + 22}{w^{2} - 5 w - 14}$