Divide Using Long Polynomial Division (120x^2+78x-90)÷(12x+15)

$(120 x^{2} + 78 x - 90) \div (12 x + 15)$

Step 1

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

$12 x$

$15$

$120 x^{2}$

$78 x$

$90$

Step 2

Divide the highest order term in the dividend $120 x^{2}$ by the highest order term in divisor $12 x$ .

					$10 x$
	$12 x$	+	$15$		$120 x^{2}$	+	$78 x$	-	$90$

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 $120 x^{2} + 150 x$

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 $- 72 x$ by the highest order term in divisor $12 x$ .

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 $- 72 x - 90$

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.

$10 x - 6$