Divide Using Long Polynomial Division (10x^2-5x-13)÷(-5x^2+6x+5)

$(10 x^{2} - 5 x - 13) \div (- 5 x^{2} + 6 x + 5)$

Step 1

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

$5 x^{2}$

$6 x$

$5$

$10 x^{2}$

$5 x$

$13$

Step 2

Divide the highest order term in the dividend $10 x^{2}$ by the highest order term in divisor $- 5 x^{2}$ .

						-	$2$
-	$5 x^{2}$	+	$6 x$	+	$5$		$10 x^{2}$	-	$5 x$	-	$13$

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 $10 x^{2} - 12 x - 10$

Step 5

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

Step 6

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

$- 2 + \frac{7 x - 3}{- 5 x^{2} + 6 x + 5}$