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w^{2}\left(4w+3\right)-7\left(4w+3\right)
Do the grouping 4w^{3}+3w^{2}-28w-21=\left(4w^{3}+3w^{2}\right)+\left(-28w-21\right), and factor out w^{2} in the first and -7 in the second group.
\left(4w+3\right)\left(w^{2}-7\right)
Factor out common term 4w+3 by using distributive property. Polynomial w^{2}-7 is not factored since it does not have any rational roots.