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4r^{2}\left(4r+7\right)-7\left(4r+7\right)
Do the grouping 16r^{3}+28r^{2}-28r-49=\left(16r^{3}+28r^{2}\right)+\left(-28r-49\right), and factor out 4r^{2} in the first and -7 in the second group.
\left(4r+7\right)\left(4r^{2}-7\right)
Factor out common term 4r+7 by using distributive property. Polynomial 4r^{2}-7 is not factored since it does not have any rational roots.