Answer
$\left( x+1 \right)\left( {{x}^{2}}+3 \right)$
Work Step by Step
${{x}^{3}}+{{x}^{2}}+3x+3$
Arranging the function in pairs,
$\left( {{x}^{3}}+{{x}^{2}} \right)+\left( 3x+3 \right)$
${{x}^{2}}\left( x+1 \right)+3\left( x+1 \right)$
Factoring out x+1:
$\left( x+1 \right)\left( {{x}^{2}}+3 \right)$
Check:
Apply the FOIL method,
$\begin{align}
& \left( x+1 \right)\left( {{x}^{2}}+3 \right)=x\cdot {{x}^{2}}+x\cdot 3+{{x}^{2}}+3 \\
& ={{x}^{3}}+3x+{{x}^{2}}+3 \\
& ={{x}^{3}}+{{x}^{2}}+3x+3
\end{align}$
Thus, the factored form of the function ${{x}^{3}}+{{x}^{2}}+3x+3$ is $\left( x+1 \right)\left( {{x}^{2}}+3 \right)$.
