Divide Using Long Polynomial Division (4x^2-10x-24)÷(2x+3)

$(4 x^{2} - 10 x - 24) \div (2 x + 3)$

Step 1

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

$2 x$

$3$

$4 x^{2}$

$10 x$

$24$

Step 2

Divide the highest order term in the dividend $4 x^{2}$ by the highest order term in divisor $2 x$ .

					$2 x$
	$2 x$	+	$3$		$4 x^{2}$	-	$10 x$	-	$24$

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 $4 x^{2} + 6 x$

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 $- 16 x$ 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 $- 16 x - 24$

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.

$2 x - 8$