Precalculus Examples

$\frac{8 x - 5}{2 x + 1}$

Step 1

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

$2 x$

$1$

$8 x$

$5$

Step 2

Divide the highest order term in the dividend $8 x$ by the highest order term in divisor $2 x$ .

					$4$
	$2 x$	+	$1$		$8 x$	-	$5$

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 $8 x + 4$

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.

$4 - \frac{9}{2 x + 1}$