Factor Theorem  : If $p(x)$ is a polynomial of degree $n > 1$ and $a$ is any real number,
                        then (i) $(x – a)$ is a factor of $p(x)$, if $p(a) = 0$, 
                    and
                        (ii) $p(a) = 0$, if $(x – a)$ is a factor of $p(x)$. 

Proof: By the Remainder Theorem, $p(x)=(x – a) q(x) + p(a)$.
(i) If $p(a) = 0$, then $p(x) = (x – a) q(x)$, which shows that $(x – a)$ is a factor of $p(x)$. 

(ii) Since $(x – a)$ is a factor of $p(x)$, $p(x) = (x – a) g(x)$ for same polynomial $g(x)$.

In this case, $p(a)$ = $(a – a) g(a)$ = 0.