Answer
The given statement is true.
Work Step by Step
The remainder theorem says that $P\left( -5 \right)$ is the remainder when $P\left( -5 \right)$ is divided by $P\left( x \right)={{x}^{3}}+7{{x}^{2}}+3x+4$.
The value of $P\left( -5 \right)$ can be evaluated by using synthetic division.
The dividend is ${{x}^{3}}+7{{x}^{2}}+3x+4$ and the divisor is $x+5$.
The constant term of the divisor 5 with the opposite sign is written to left.
The coefficients of the dividend $1,7,3,4$ are written to the right.
Evaluate the value of $\left( {{x}^{3}}+7{{x}^{2}}+3x+4 \right)\div \left( x+5 \right)$ using synthetic division as follows.
$\begin{align}
& \left. {\underline {\,
-5 \,}}\! \right| \text{ 1 7 3 4} \\
& \text{ }\underline{\text{ }-5\text{ }-10\text{ 35}} \\
& \text{ 1 2 }-7\text{ 39} \\
\end{align}$
