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