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