Answer
True.
Work Step by Step
The Factor Theorem states that for any polynomial function $f(x)$, if $x-k$ is factor of $f(x)$, then $f(k)=0$, and that if $f(k) =0$, then $x-k$ is a factor of $f(x)$.
Since $x-1$ is a factor of $f(x)$, then, by the factor theorem, $f(1)=0$.
Hencec, the given statemebt is true.