Question

find the quotient and remainder using long division.
$\frac{-8x^{3}+10x^{2}-12x+15}{4x - 5}$
the quotient is
the remainder is
question help: video

Explanation:

Step1: Divide leading terms

$\frac{-8x^3}{4x} = -2x^2$

Step2: Multiply divisor by result

$-2x^2(4x - 5) = -8x^3 + 10x^2$

Step3: Subtract from dividend

$(-8x^3 + 10x^2 - 12x + 15) - (-8x^3 + 10x^2) = -12x + 15$

Step4: Divide new leading terms

$\frac{-12x}{4x} = -3$

Step5: Multiply divisor by result

$-3(4x - 5) = -12x + 15$

Step6: Subtract to find remainder

$(-12x + 15) - (-12x + 15) = 0$

Answer:

The quotient is $-2x^2 - 3$
The remainder is $0$