Question

Find the quotient and remainder using long division.

$$dfrac{x^3 + 3x + 1}{x^2 – x + 4}

$$

EXPERT ANSWER

Find the quotient and remainder using long division.

$$displaystyle dfrac{x^3 + 3x + 1}{x^2 – x + 4}

$$

Solution:

$$begin{align}

quadquadquadquad &::: x+1& rightarrow text{Quotient}\

x^2-x+4&overline{)x^3+0x^2+3x+1}\

-::::& :: x^{3}-:x^{2}+4x\

& overline{quadquad:: ::x^2-::x+1}\

-::::& quad: quad quad x^2-x+4\

& overline{quadquadquadquadquad::::-3}& rightarrow text{Remainder}\

end{align}

$$

Hence, the quotient is equal to {eq}displaystyle{boxed{color{blue}{ x+1 }}}

{/eq} and the remainder is equal to {eq}displaystyle{boxed{color{blue}{ frac{-3}{x^2-x+4}