Divide Using Long Polynomial Division (7x-3x^2+5)/(4+2x^2)

$\frac{7 x - 3 x^{2} + 5}{4 + 2 x^{2}}$

Step 1

Reorder $7 x$ and $- 3 x^{2}$ .

$\frac{- 3 x^{2} + 7 x + 5}{4 + 2 x^{2}}$

Step 2

Reorder $4$ and $2 x^{2}$ .

$\frac{- 3 x^{2} + 7 x + 5}{2 x^{2} + 4}$

Step 3

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

$2 x^{2}$

$0 x$

$4$

$3 x^{2}$

$7 x$

$5$

Step 4

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

						-	$\frac{3}{2}$
	$2 x^{2}$	+	$0 x$	+	$4$	-	$3 x^{2}$	+	$7 x$	+	$5$

Step 5

Multiply the new quotient term by the divisor.

Step 6

The expression needs to be subtracted from the dividend, so change all the signs in $- 3 x^{2} + 0 - 6$

Step 7

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

Step 8

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

$- \frac{3}{2} + \frac{7 x + 11}{2 x^{2} + 4}$