Divide Using Long Polynomial Division (3x^2-13x-10)/(x-5)

$\frac{(3 x^{2} - 13 x - 10)}{(x - 5)}$

Step 1

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

$x$

$5$

$3 x^{2}$

$13 x$

$10$

Step 2

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

					$3 x$
	$x$	-	$5$		$3 x^{2}$	-	$13 x$	-	$10$

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 $3 x^{2} - 15 x$

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 $2 x$ by the highest order term in divisor $x$ .

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 $2 x - 10$

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.

$3 x + 2$