Answer
The required solution is True.
Work Step by Step
We know that according to the synthetic division theorem,
$\begin{align}
& \left. {\underline {\,
-1 \,}}\! \right| \text{ }3\text{ }-4\text{ }2\text{ }-1 \\
& \text{ }\underline{\text{ }-3\text{ }7\text{ }-9} \\
& \text{ }\underbrace{3}_{\text{coe}\text{. of }{{x}^{2}}}\text{ }\underbrace{-7}_{\text{coe}\text{. of }{{x}^{1}}}\text{ }\underbrace{9}_{\text{coe}\text{. of }{{x}^{0}}}\text{ }\underbrace{-10}_{\text{Remainder}} \\
\end{align}$.
Thus,
$\begin{align}
& \left. {\underline {\,
-1 \,}}\! \right| \text{ }3\text{ }-4\text{ }2\text{ }-1 \\
& \text{ }\underline{\text{ }-3\text{ }7\text{ }-9} \\
& \text{ }3\text{ }-7\text{ }9\text{ }-10 \\
\end{align}$
Implies:
$\frac{3{{x}^{3}}-4{{x}^{2}}+2x-1}{x+1}=\left( 3{{x}^{2}}-7x+9 \right)-\frac{10}{x+1}$.
