Precalculus Examples

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

Step 1

Add $3 x$ and $5 x$ .

$\frac{8 x - 2}{x + 5}$

Step 2

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

$x$

$5$

$8 x$

$2$

Step 3

Divide the highest order term in the dividend $8 x$ by the highest order term in divisor $x$ .

					$8$
	$x$	+	$5$		$8 x$	-	$2$

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 $8 x + 40$

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.

$8 - \frac{42}{x + 5}$