Question

Simplify using long division.

{eq}(8b^3 – 6) div (2b – 1)

{/eq}

EXPERT ANSWER

Simplify:

$$frac{8b^3:-:6}{2b:-:1}

$$

Solution:

$$begin{align}

&quad 4b^2+2b+1 quad rightarrow text{Quotient}\

2b-1&:overline{ ): 8b^3+ 0b^2+ 0b-6}\

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

&quadquadquad ::2b^2-0b\

&-quadquad:underline{2b^2-2bquadquad:}\

&quadquadquad quadquad::::::2b-6\

&quadquadquad quadquad::::::underline{2b-1}\

&quadquadquadquadquadquadquad ::-5 quad rightarrow text{Remainder}

end{align}

$$

Therefore, the answer is equal to {eq}displaystyle{boxed{color{blue}{4b^2+2b+1-frac{5}{2b-1}}}}

{/eq}.

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