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y^{2}\left(y+7\right)+5\left(y+7\right)
Do the grouping y^{3}+7y^{2}+5y+35=\left(y^{3}+7y^{2}\right)+\left(5y+35\right), and factor out y^{2} in the first and 5 in the second group.
\left(y+7\right)\left(y^{2}+5\right)
Factor out common term y+7 by using distributive property. Polynomial y^{2}+5 is not factored since it does not have any rational roots.