Question

Simplify using long division.

{eq}(-72 – 4x^2 + 8x^3 – 36x) div (x – 3)

{/eq}

EXPERT ANSWER

Simplify using long division.

$$frac{-72 – 4x^2 + 8x^3 – 36x}{x – 3}

$$

Solution:

Rearrange the dividend starting with the variable with the highest degree to lowest.

$$begin{align}

&quad 8x^2+20x+24\

x-3&:overline{ ): 8x^3- 4x^2- 36x-72}\

-&:::underline{8x^3-24x^2quadquadquad}\

&quadquadquad ::20x^2-36x\

&-quadquad:underline{20x^2-60xquadquad::}\

&quadquadquad quadquadquad::::24x-72\

&quadquadquad quadquadquad::::underline{24x-72}\

&quadquadquadquadquadquadquad quadquadquad0

end{align}

$$

Hence, the quotient is equal to {eq}displaystyle{boxed{color{blue}{ 8x^2+20x+24}}}

{/eq}.

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