Answer
$3(x-6)(x+2)$
Work Step by Step
Factor out the GCF, which is $3$, to obtain:
$3x^2-12x-36=3(x^2-4x-12)$
Look for factors of $-12$ whose sum is equal to the middle term's coefficient $(-4)$. The factors are $-6$ and $2$.
Use the factors found to rewrite the middlle terms $-4x$ as $-6x+2x$.
$=3(x^2-6x+2x-12)$
Group the first two terms together and group the last two terms terms.
$=3[(x^2-6x)+(2x-12)]$
Factor out the GCF in each group.
$=3[x(x-6)+2(x-6)]$
Factor out $(x-6)$.
$=3(x-6)(x+2)$
Hence, the completely factored form of the given expression is $3(x-6)(x+2)$.
