Divide Using Long Polynomial Division (2x^2-3x+5)÷(2x-3)

$(2 x^{2} - 3 x + 5) \div (2 x - 3)$

Step 1

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

$2 x$

$3$

$2 x^{2}$

$3 x$

$5$

Step 2

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

					$x$
	$2 x$	-	$3$		$2 x^{2}$	-	$3 x$	+	$5$

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 $2 x^{2} - 3 x$

Step 5

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

Step 6

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

Step 7

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

$x + \frac{5}{2 x - 3}$