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5\left(u^{5}+3u^{4}+4u^{3}\right)
Factor out 5.
u^{3}\left(u^{2}+3u+4\right)
Consider u^{5}+3u^{4}+4u^{3}. Factor out u^{3}.
5u^{3}\left(u^{2}+3u+4\right)
Rewrite the complete factored expression. Polynomial u^{2}+3u+4 is not factored since it does not have any rational roots.