Answer
$(x+6)^2$
Work Step by Step
The leading coefficient is $1$ so just look for factors of $36$ whose sum is equal to the coefficient of the middle term $(12)$. The factors are $6$ and $6$.
Rewrite the middle term $12x$ as $6x+6x$ to obtain:
$x^2+12x+36=x^2+6x+6x+36$
Group the first two terms and group the last two terms to obtain:
$=(x^2+6x)+(6x+36)$
Factor out the GCF in each group.
$=x(x+6)+6(x+6)$
Factor out $(x+6)$.
$=(x+6)(x+6)$
$=(x+6)^2$
Hence, the completely factored form of the given expression is $(x+6)^2$.
