Answer
The roots of the polynomial function are $\left\{ -1,\,\,-2,\,\,2 \right\}$.
Work Step by Step
Let us consider the function ${{x}^{3}}+{{x}^{2}}=4x+4$.
Simplifying,
$\begin{align}
& {{x}^{3}}+{{x}^{2}}=4x+4 \\
& {{x}^{3}}+{{x}^{2}}-4x-4=0 \\
& \left( x+1 \right)\left( {{x}^{2}}-4 \right)=0 \\
& \left( x+1 \right)\left( x+2 \right)\left( x-2 \right)=0
\end{align}$
Therefore,
$x=-1,\,\,-2,\,\,2$
Hence, the roots are $-1,\,\,-2,\,\,2$
