Divide Using Long Polynomial Division (6x^2+11x-35)÷(3x-5)

$(6 x^{2} + 11 x - 35) \div (3 x - 5)$

Step 1

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

$3 x$

$5$

$6 x^{2}$

$11 x$

$35$

Step 2

Divide the highest order term in the dividend $6 x^{2}$ by the highest order term in divisor $3 x$ .

					$2 x$
	$3 x$	-	$5$		$6 x^{2}$	+	$11 x$	-	$35$

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 $6 x^{2} - 10 x$

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 $21 x$ 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 $21 x - 35$

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.

$2 x + 7$