Answer
$3y(y-8)(y+2)$
Work Step by Step
Factor out $3y$.
$3y^3-18y^2-48y=3y(y^2-6y-16)$
Look for factors of $-16$ whose sum is equal to the middle term's coefficient $(-6)$. The factors are $-8$ and $2$.
Use the factors found to rewrite the middle term $-6y$ as $-8y+2y$.
$=3y(y^2-8y+2y-16)$
Group the first two terms together and group the last two terms together to obtain:
$=3y[(y^2-8y)+(2y-16)]$
Factor out the GCF in each group.
$=3y[y(y-8)+2(y-8)]$
Factor out $(y-8)$.
$=3y(y-8)(y+2)$
Hence, the completely factored form of the given expression is $3y(y-8)(y+2)$.
