Pre-Algebra Examples

$\frac{x^{2} - 2 x - 14}{2 - x}$

Step 1

Reorder $2$ and $- x$ .

$\frac{x^{2} - 2 x - 14}{- x + 2}$

Step 2

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

$x$

$2$

$x^{2}$

$2 x$

$14$

Step 3

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

				-	$x$
-	$x$	+	$2$		$x^{2}$	-	$2 x$	-	$14$

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 $x^{2} - 2 x$

Step 6

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

Step 7

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

Step 8

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

$- x - \frac{14}{- x + 2}$