A non-zero polynomial $f(x)$ of degree 3 has roots at $x = 1, x = 2$ and $x = 3$. Which one of the following must be TRUE?

Since $f(x)$ is a polynomial of degree 3 with roots at $x = 1, 2, 3$, it can be written as:

where $c$ is a non-zero real constant ($c \neq 0$).

Evaluating $f(x)$ at $x = 0$ and $x = 4$:

Now, compute their product:

Since $c \neq 0$, $c^2 > 0$, which means:

Also, $f(0) + f(4) = -6c + 6c = 0$, which rules out (C) and (D). Therefore, option (A) must be TRUE.