Ans: D
Since $f(x)$ is divisible by $2x+1$, then by the factor theorem, we have
Since $f(x)$ is divisible by $2x+1$, then by the factor theorem, we have
$\begin{array}{rcl}
f(\dfrac{-1}{2}) & = & 0 \\
2(\dfrac{-1}{2})^2 + a (\dfrac{-1}{2}) – 3 & = & 0 \\
\dfrac{1}{2} – \dfrac{a}{2} -3 & = & 0 \\
a & = & -5
\end{array}$
Hence, $f(x)=2x^2-5x-3$.
Then by the remainder theorem, the required remainder
$\begin{array}{cl}
= & f(-5) \\
= & 2(-5)^2-5(-5)-3 \\
= & 72
\end{array}$
