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4x^{2}\left(5x+3\right)+5x+3
Do the grouping 20x^{3}+12x^{2}+5x+3=\left(20x^{3}+12x^{2}\right)+\left(5x+3\right), and factor out 4x^{2} in 20x^{3}+12x^{2}.
\left(5x+3\right)\left(4x^{2}+1\right)
Factor out common term 5x+3 by using distributive property. Polynomial 4x^{2}+1 is not factored since it does not have any rational roots.