The function $f$ is defined by a polynomial. Some of the values of $x$ and $f(x)$ are given in the table below. Which of the following must be a factor of $f(x)$ ?

Question

$\begin{array}{1 1} (a)\; x-2 \\ (b)\; x-4 \\(c)\; x-1 \\ (d)\; x-6 \end{array}$