Ans: D
Let $f(x) = 2x^4 +kx^3 -4x -16$. Since $f(x)$ is divisible by $2x + k$, then by the factor theorem, we have
Let $f(x) = 2x^4 +kx^3 -4x -16$. Since $f(x)$ is divisible by $2x + k$, then by the factor theorem, we have
$\begin{array}{rcl}
f(\dfrac{-k}{2}) & = & 0 \\
2(\dfrac{-k}{2})^4 + k(\dfrac{-k}{2})^3 – 4(\dfrac{-k}{2}) – 16 & = & 0 \\
\dfrac{k^4}{8} – \dfrac{k^4}{8} +2k – 16 & = & 0 \\
2k & = & 16 \\
k & = & 8
\end{array}$
