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y^{2}\left(y+9\right)+4\left(y+9\right)
Do the grouping y^{3}+9y^{2}+4y+36=\left(y^{3}+9y^{2}\right)+\left(4y+36\right), and factor out y^{2} in the first and 4 in the second group.
\left(y+9\right)\left(y^{2}+4\right)
Factor out common term y+9 by using distributive property. Polynomial y^{2}+4 is not factored since it does not have any rational roots.