Examine the validity of the following statement: $(x+3)$ is a factor of $(x^{2}+10x+21)$.

(TRUE) To determine if $(x+3)$ is a factor of $p(x) = x^{2}+10x+21$,we use the Factor Theorem.
According to the Factor Theorem,$(x-a)$ is a factor of $p(x)$ if $p(a) = 0$.
Here,$(x+3) = (x - (-3))$,so $a = -3$.
Now,calculate $p(-3)$:
$p(-3) = (-3)^{2} + 10(-3) + 21$
$p(-3) = 9 - 30 + 21$
$p(-3) = 30 - 30 = 0$.
Since $p(-3) = 0$,the statement is True.