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