Ans: A
Let $f(x)=x^3+5x^2+3kx-k$. Since $f(x)$ is divisible by $x-1$, then $f(1)=0$. Hence, we have
Let $f(x)=x^3+5x^2+3kx-k$. Since $f(x)$ is divisible by $x-1$, then $f(1)=0$. Hence, we have
$\begin{array}{rcl}
f(1) & = & 0 \\
(1)^3+5(1)^2+3k(1)- k & = & 0 \\
6 +2k & = & 0 \\
2k & = & -6 \\
k & = & -3
\end{array}$
