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4y^{2}\left(4y+7\right)+5\left(4y+7\right)
Do the grouping 16y^{3}+28y^{2}+20y+35=\left(16y^{3}+28y^{2}\right)+\left(20y+35\right), and factor out 4y^{2} in the first and 5 in the second group.
\left(4y+7\right)\left(4y^{2}+5\right)
Factor out common term 4y+7 by using distributive property. Polynomial 4y^{2}+5 is not factored since it does not have any rational roots.