Algebra Examples

$(2 x^{3} - x^{2} - 24 x + 12) \div (2 x - 1)$

Step 1

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

$2 x$

$1$

$2 x^{3}$

$x^{2}$

$24 x$

$12$

Step 2

Divide the highest order term in the dividend $2 x^{3}$ by the highest order term in divisor $2 x$ .

					$x^{2}$
	$2 x$	-	$1$		$2 x^{3}$	-	$x^{2}$	-	$24 x$	+	$12$

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

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

Divide the highest order term in the dividend $- 24 x$ by the highest order term in divisor $2 x$ .

Step 8

Multiply the new quotient term by the divisor.

Step 9

The expression needs to be subtracted from the dividend, so change all the signs in $- 24 x + 12$

Step 10

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

Step 11

Since the remander is $0$ , the final answer is the quotient.

$x^{2} + 0 x - 12$