Ans: A
Since $f(x)$ is divisible by $(x-1)$, by the division algorithm we have
Since $f(x)$ is divisible by $(x-1)$, by the division algorithm we have
$\begin{array}{rcl}
f(x) & = & (x-1)Q(x),
\end{array}$
where $Q(x)$ is an polynomial. Hence, we have
$\begin{array}{rcl}
f(2x+1) & = & [(2x+1)-1]Q(2x+1) \\
& = & 2xQ(2x+1)
\end{array}$
Therefore, $x$ must be a factor of $f(2x+1)$.
