Factor LaTeX: \displaystyle 12 x^{3} - 32 x^{2} - 27 x + 72 .

Grouping the first two terms and factoring out their GCF, LaTeX: \displaystyle 4 x^{2} , gives LaTeX: \displaystyle 4 x^{2}(3 x - 8) . Grouping the last two terms and factoring out their GCF, LaTeX: \displaystyle -9 , gives LaTeX: \displaystyle -9(3 x - 8) . The polynomial now has a common binomial factor of LaTeX: \displaystyle 3 x - 8 . This gives LaTeX: \displaystyle 4 x^{2} \left(3 x - 8\right) -9 \cdot \left(3 x - 8\right) = \left(3 x - 8\right) \left(4 x^{2} - 9\right) . The quadratic factor can be factored using the difference of squares to give LaTeX: \displaystyle \left(2 x - 3\right) \left(2 x + 3\right) \left(3 x - 8\right).