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5x^{2}\left(7x-4\right)+7x-4
Do the grouping 35x^{3}-20x^{2}+7x-4=\left(35x^{3}-20x^{2}\right)+\left(7x-4\right), and factor out 5x^{2} in 35x^{3}-20x^{2}.
\left(7x-4\right)\left(5x^{2}+1\right)
Factor out common term 7x-4 by using distributive property. Polynomial 5x^{2}+1 is not factored since it does not have any rational roots.