### Theory:

Factor Theorem: If $p\left(x\right)$ is a polynomial of degree $$n > 1$$ and $$a$$ is any real number, then:

(i) is a factor of $p\left(x\right)$, if , and

(ii), if  is a factor of $p\left(x\right)$.

This is an extension to the remainder theorem where the remainder is $0$, which is .
Example:
Examine whether   is factor of .

To find is a factor of  or not.

As, result of factor theorem  is factor of $$p(x)$$ if .

The zero of  is $$x+2 = 0$$. That is, $$x = -2$$.

Therefore,  is factor of .
Important!
When  may be a factor of $p\left(x\right)$ then .