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3x^{2}\left(4x-3\right)-4\left(4x-3\right)
Do the grouping 12x^{3}-9x^{2}-16x+12=\left(12x^{3}-9x^{2}\right)+\left(-16x+12\right), and factor out 3x^{2} in the first and -4 in the second group.
\left(4x-3\right)\left(3x^{2}-4\right)
Factor out common term 4x-3 by using distributive property. Polynomial 3x^{2}-4 is not factored since it does not have any rational roots.