Ans: B
Let $f(x)=x^3+4x^2+kx-12$.
Let $f(x)=x^3+4x^2+kx-12$.
Since $f(x)$ is divisible by $x+3$, then the by factor theorem we have
$\begin{array}{rcl}
f(-3) & = & 0 \\
(-3)^3+4(-3)^2+k(-3)-12 & = & 0 \\
-3k – 3 & = & 0 \\
k & = & -1
\end{array}$
