Answer
$2b^3-2b^2+3$
Work Step by Step
The long division method below shows the result of $
(2b^6+2b^5-4b^4+b^3+8b^2-3)\div(b^3+2b^2-1)
.$
$$\begin{array}{l}
\phantom{b^3+2b^2-1)}2b^3-2b^2\phantom{-4b^4}\,\,+\phantom{2}3
\\
\color{blue}{b^3+2b^2-1}\color{black}{\overline{\smash{)}2b^6+2b^5-4b^4+\phantom{2}b^3+8b^2-3}}
\\
\phantom{b^3+2b^2-1)}\underline{2b^6+4b^5\phantom{-4b^4\,\,}-2b^3}
\\
\phantom{b^3+2b^2-1)2b^6}-2b^5-4b^4+3b^3+8b^2
\\
\phantom{b^3+2b^2-1)2b^\,6}\underline{-\,2b^5-4b^4\phantom{+3b^3\,\,}+2b^2}
\\
\phantom{b^3+2b^2-1)2b^\,6-2b^5-4b^4+}3b^3+6b^2-3
\\
\phantom{b^3+2b^2-1)2b^\,6-2b^5-4b^4+}\underline{3b^3+6b^2-3}
\\
\color{red}{\phantom{b^3+2b^2-1)2b^\,6-2b^5-4b^4+3b^3+6b^2-}0}
\end{array}$$Hence, the quotient is $2b^3-2b^2+3$.