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