Answer
(a)
Work Step by Step
The given synthetic division is:-
$\begin{matrix}
&-- &-- &--&--& \\
-5) &2&3&-38&-15& & \\
& &-10 &35 &15 && \\
& -- & -- & --& -- && \\
& 2 & -7& -3 &0 & \\
\end{matrix}$
We have $c=-5$, so the divisor is $x+5$.
Use coefficients on the right side as dividend in descending powers of $x$.
The dividend is $2x^3+3x^2-38x-15$
The remainder, which is found at the bottom right, is zero.
Hence, $(x+5)$ is a factor of $2x^3+3x^2-38x-15$.
The correct option is $(a)$.
