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