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4n^{2}\left(5n+1\right)+3\left(5n+1\right)
Do the grouping 20n^{3}+4n^{2}+15n+3=\left(20n^{3}+4n^{2}\right)+\left(15n+3\right), and factor out 4n^{2} in the first and 3 in the second group.
\left(5n+1\right)\left(4n^{2}+3\right)
Factor out common term 5n+1 by using distributive property. Polynomial 4n^{2}+3 is not factored since it does not have any rational roots.