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