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