Divide Using Long Polynomial Division (3x^2+2x-20)÷(x^2-8x+12)

$(3 x^{2} + 2 x - 20) \div (x^{2} - 8 x + 12)$

Step 1

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

$x^{2}$

$8 x$

$12$

$3 x^{2}$

$2 x$

$20$

Step 2

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

							$3$
	$x^{2}$	-	$8 x$	+	$12$		$3 x^{2}$	+	$2 x$	-	$20$

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 $3 x^{2} - 24 x + 36$

Step 5

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

Step 6

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

$3 + \frac{26 x - 56}{x^{2} - 8 x + 12}$