Answer
a) $\frac{27 x^2-6 x-8}{3 x-2}= 9x+4$
b) $ (3 x-2)\cdot (9x+4)$
Work Step by Step
Given \begin{equation}
\left(27 x^2-6 x-8\right) \div(3 x-2).
\end{equation} Use long division. $$
\begin{array}{r}
9x+4\phantom{)} \\
3 x-2{\overline{\smash{\big)}\,27 x^2-6 x-8\phantom{)}}}\\
\underline{-~\phantom{(}(27x^2-18x)\phantom{-b)}}\\
0+12x-8\phantom{)}\\
\underline{-~\phantom{()}(12x-8)}\\
0\phantom{)}
\end{array}
$$ a) The solution is \begin{equation}
\frac{27 x^2-6 x-8}{3 x-2}= 9x+4.
\end{equation} b) The prime factor decomposition is $$ (3 x-2)\cdot (9x+4).$$
