Pre-Algebra Examples

$\frac{4 x - x^{2}}{x^{2} + 2 x - 8}$

Step 1

Reorder $4 x$ and $- x^{2}$ .

$\frac{- x^{2} + 4 x}{x^{2} + 2 x - 8}$

Step 2

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

$x^{2}$

$2 x$

$8$

$x^{2}$

$4 x$

$0$

Step 3

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

						-	$1$
	$x^{2}$	+	$2 x$	-	$8$	-	$x^{2}$	+	$4 x$	+	$0$

Step 4

Multiply the new quotient term by the divisor.

Step 5

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

Step 6

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

Step 7

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

$- 1 + \frac{6 x - 8}{x^{2} + 2 x - 8}$