Answer
True.
Work Step by Step
By the Division Algorithm for polynomials if a polynomial $f(x)$ (with degree $n$) is divided by a polynomial $(x-c)$ (with degree $1$), then we get a polynomial with degree $n-1$ (here $p(x)$) plus $\frac{r(x)}{x-c}=\frac{f(c)}{x-c}$. Thus the statement is true.
