Divide Using Long Polynomial Division (-24x^2-22x+7)÷(-4x+1)

$(- 24 x^{2} - 22 x + 7) \div (- 4 x + 1)$

Step 1

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

$4 x$

$1$

$24 x^{2}$

$22 x$

$7$

Step 2

Divide the highest order term in the dividend $- 24 x^{2}$ by the highest order term in divisor $- 4 x$ .

					$6 x$
-	$4 x$	+	$1$	-	$24 x^{2}$	-	$22 x$	+	$7$

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 $- 24 x^{2} + 6 x$

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 $- 28 x$ by the highest order term in divisor $- 4 x$ .

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 $- 28 x + 7$

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.

$6 x + 7$