Answer
$x^2+5x-4$
Work Step by Step
Given \begin{equation}
\left(x^3+7 x^2+6 x-8\right) \div(x+2).
\end{equation} Use long division. $$
\begin{array}{r}
x^2+5x-4\phantom{)} \\
x+2{\overline{\smash{\big)}\,x^3+7 x^2+6 x-8\phantom{)}}}\\
\underline{-~\phantom{(}(x^3+2x^2)\phantom{-b)}}\\
0+5x^2+6x\phantom{)}\\
\underline{-~\phantom{()}(5x+10x)}\\
-4x-8\phantom{)}\\
\underline{-~\phantom{()}(-4x-8)}\\
0\phantom{)}
\end{array}
$$ The solution is \begin{equation}
\frac{x^3+7 x^2+6 x-8}{x+2}=x^2+5x-4
\end{equation}
