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

$(6 x \cdot 2 + 11 x - 35) \div (3 x - 5)$

Step 1

Expand $6 x \cdot 2 + 11 x - 35$ .

Move $x$ .

$\frac{6 \cdot (2 x) + 11 x - 35}{3 x - 5}$

Multiply $6$ by $2$ .

$\frac{12 x + 11 x - 35}{3 x - 5}$

Add $12 x$ and $11 x$ .

$\frac{23 x - 35}{3 x - 5}$

Step 2

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

$3 x$

$5$

$23 x$

$35$

Step 3

Divide the highest order term in the dividend $23 x$ by the highest order term in divisor $3 x$ .

					$\frac{23}{3}$
	$3 x$	-	$5$		$23 x$	-	$35$

Step 4

Multiply the new quotient term by the divisor.

Step 5

The expression needs to be subtracted from the dividend, so change all the signs in $23 x - \frac{115}{3}$

Step 6

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

Step 7

The final answer is the quotient plus the remainder over the divisor.

$\frac{23}{3} + \frac{10}{3 (3 x - 5)}$