Divide Using Long Polynomial Division (-3x^2+20x-12)÷(x-6)

$(- 3 x^{2} + 20 x - 12) \div (x - 6)$

Step 1

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

$x$

$6$

$3 x^{2}$

$20 x$

$12$

Step 2

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

				-	$3 x$
	$x$	-	$6$	-	$3 x^{2}$	+	$20 x$	-	$12$

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 $- 3 x^{2} + 18 x$

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 $2 x - 12$

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.

$- 3 x + 2$