Algebra Examples

$(- 17 + 4 x^{2}) \div (- 2 x^{2} + 3 x)$

Step 1

Reorder $- 17$ and $4 x^{2}$ .

$\frac{4 x^{2} - 17}{- 2 x^{2} + 3 x}$

Step 2

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

$2 x^{2}$

$3 x$

$0$

$4 x^{2}$

$0 x$

$17$

Step 3

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

						-	$2$
-	$2 x^{2}$	+	$3 x$	+	$0$		$4 x^{2}$	+	$0 x$	-	$17$

Step 4

Multiply the new quotient term by the divisor.

Step 5

The expression needs to be subtracted from the dividend, so change all the signs in $4 x^{2} - 6 x + 0$

Step 6

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

Step 7

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

$- 2 + \frac{6 x - 17}{- 2 x^{2} + 3 x}$