Pre-Algebra Examples

$\frac{3 x^{3} + 9 x^{2} - 14}{x + 3}$

Step 1

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

$x$

$3$

$3 x^{3}$

$9 x^{2}$

$0 x$

$14$

Step 2

Divide the highest order term in the dividend $3 x^{3}$ by the highest order term in divisor $x$ .

					$3 x^{2}$
	$x$	+	$3$		$3 x^{3}$	+	$9 x^{2}$	+	$0 x$	-	$14$

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 $3 x^{3} + 9 x^{2}$

Step 5

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

Step 6

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

Step 7

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

$3 x^{2} - \frac{14}{x + 3}$