Let $f(X)$ be a real polynomial and let $a\in{\textbf{R}}$. Then the remainder on dividing $f(X)$ by $X-a$ is $f(a)$, so

for some real polynomial $q(X)$.

In particular, suppose that $f(a)=0$. Then $a$ is a zero of $f(X)$ (or root of $f(X)=0).$ The graph of $f(x)$ intersects with the $x$ axis at $x=b$, and $X-a$ divides $f(X)$.

Factorize $f(X)=X^{3}-3X^{2}-4X+12$ as a product of linear factors.