Algebra Examples

$\frac{x^{2} - 25}{x^{2} - 3 x - 10}$

Step 1

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

$x^{2}$

$3 x$

$10$

$x^{2}$

$0 x$

$25$

Step 2

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

							$1$
	$x^{2}$	-	$3 x$	-	$10$		$x^{2}$	+	$0 x$	-	$25$

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 $x^{2} - 3 x - 10$

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.

$1 + \frac{3 x - 15}{x^{2} - 3 x - 10}$