Answer
The required value is $\left( {{x}^{2}}+3 \right)\left( x+2 \right)$.
Work Step by Step
Consider the expression,
${{x}^{3}}+2{{x}^{2}}+3x+6$
The given expression can be evaluated as:
$\begin{align}
& {{x}^{3}}+2{{x}^{2}}+3x+6={{x}^{^{2}}}\left( x+2 \right)+3\left( x+2 \right) \\
& =\left( {{x}^{2}}+3 \right)\left( x+2 \right)
\end{align}$
Therefore, the value of ${{x}^{3}}+2{{x}^{2}}+3x+6$ is $\left( {{x}^{2}}+3 \right)\left( x+2 \right)$.
