Question

Divide the polynomial: {eq}(3x^4 – 25x^2 – 20) div (x – 3)

{/eq}.

EXPERT ANSWER

Given:

- Dividend: {eq}3x^4-25x^2-20
{/eq}

Solution:

$$begin{align}

quadquadquadquad &3x^3-9x^2+52x-156rightarrow text{Quotient}\

x-3&overline{)3x^4-25x^2-20}\

& : 3x^4quadquadquadquadquadquad-9x^3\

& overline{quadquadquad -25x^2-20-9x^3}\

& quadquadquad+27x^2quadquad-9x^3\

& overline{quadquadquadquad+52x^2-20}\

& quadquadquadquad+52x^2quadquadquadquad-156x\

& overline{quadquadquadquadquadquadquad-20quadquad-156x}\

& quadquadquadquadquadquad+468quadquad-156x\

& overline{quadquadquadquadquadquad -488}rightarrow text{Remainder}\

end{align}

$$

Therefore, the quotient is {eq}boxed{3x^3-9x^2+52x-156-frac{488}{x-3}}

{/eq}.

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