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