Answer
$y^2(y+6)(y+5)$
Work Step by Step
Factor out $y^2$.
$y^4+11y^3+30y^2=y^2(y^2+11y+30)$
Look for factors of $30$ whose sum is equal to the middle term's coefficient $(11)$, The factors are $6$ and $5$.
Use the factors found to rewrite the middle term $11y$ as $6y+5y$.
$=y^2(y^2+6y+5y+30)$
Group the first two terms together and group the last two terms together to obtain:
$=y^2[(y^2+6y)+(5y+30)]$
Factor out the GCF in each group.
$=y^2[y(y+6)+5(y+6)]$
Factor out $(y+6)$.
$=y^2(y+6)(y+5)$
Hence, the completely factored form of the given expression is $y^2(y+6)(y+5)$.
