Answer
$t^2+6t+12$
Work Step by Step
Given \begin{equation}
\begin{aligned}
\left(t^3+4 t^2-24\right) \div(t-2).
\end{aligned}
\end{equation} Use synthetic division. \begin{equation}
\begin{array}{r|rrrr}
2&1 & 4 & 0 &-24 \\
& & 2 & 12& 24 \\
\hline &1 & 6 & 12 & 0
\end{array}
\end{equation} The solution is \begin{equation}
\begin{aligned}
\frac{t^3+4 t^2-24}{t-2}=t^2+6t+12.
\end{aligned}
\end{equation}
