Divide Using Long Polynomial Division (20x^2-13x+2)/(4x-1)

$\frac{20 x^{2} - 13 x + 2}{4 x - 1}$

Step 1

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

$4 x$

$1$

$20 x^{2}$

$13 x$

$2$

Step 2

Divide the highest order term in the dividend $20 x^{2}$ by the highest order term in divisor $4 x$ .

					$5 x$
	$4 x$	-	$1$		$20 x^{2}$	-	$13 x$	+	$2$

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 $20 x^{2} - 5 x$

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 $- 8 x$ by the highest order term in divisor $4 x$ .

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 $- 8 x + 2$

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.

$5 x - 2$