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x^{3}\left(2x^{2}+1\right)+3\left(2x^{2}+1\right)
Do the grouping 2x^{5}+x^{3}+6x^{2}+3=\left(2x^{5}+x^{3}\right)+\left(6x^{2}+3\right), and factor out x^{3} in the first and 3 in the second group.
\left(2x^{2}+1\right)\left(x^{3}+3\right)
Factor out common term 2x^{2}+1 by using distributive property. The following polynomials are not factored since they do not have any rational roots: 2x^{2}+1,x^{3}+3.