Answer
a) $\frac{6 x^2-47 x-8}{x-8}=6x+1$
b) $ (x-8)\cdot (6x+1)$
Work Step by Step
Given \begin{equation}
\begin{aligned}
\left(6 x^2-47 x-8\right) \div(x-8).
\end{aligned}
\end{equation} Use synthetic division.
\begin{equation}
\begin{array}{r|rrr}
8&6 & -47 & -8\\
& & 48 & 8\\
\hline &6& 1 & 0
\end{array}
\end{equation} a) The solution is \begin{equation}
\begin{aligned}
\frac{6 x^2-47 x-8}{x-8}=6x+1.
\end{aligned}
\end{equation}
b) The prime factor decomposition is $$ (x-8)\cdot (6x+1).$$