Find the Quotient (12x^2-10x-12)÷(3x+2)

$(12 x^{2} - 10 x - 12) \div (3 x + 2)$

Step 1

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

$3 x$

$2$

$12 x^{2}$

$10 x$

$12$

Step 2

Divide the highest order term in the dividend $12 x^{2}$ by the highest order term in divisor $3 x$ .

					$4 x$
	$3 x$	+	$2$		$12 x^{2}$	-	$10 x$	-	$12$

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 $12 x^{2} + 8 x$

Step 5

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

Step 6

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

Step 7

Divide the highest order term in the dividend $- 18 x$ by the highest order term in divisor $3 x$ .

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 $- 18 x - 12$

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.

$4 x - 6$