Divide (8y^2-4y+1)/(2y-1)

$\frac{8 y^{2} - 4 y + 1}{2 y - 1}$

Step 1

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

$2 y$

$1$

$8 y^{2}$

$4 y$

$1$

Step 2

Divide the highest order term in the dividend $8 y^{2}$ by the highest order term in divisor $2 y$ .

					$4 y$
	$2 y$	-	$1$		$8 y^{2}$	-	$4 y$	+	$1$

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 $8 y^{2} - 4 y$

Step 5

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

Step 6

Pull the next term from the original dividend down into the current dividend.

Step 7

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

$4 y + \frac{1}{2 y - 1}$