Factor LaTeX: \displaystyle 27 x^{3} + 9 x^{2} - 12 x - 4 .

Grouping the first two terms and factoring out their GCF, LaTeX: \displaystyle 9 x^{2} , gives LaTeX: \displaystyle 9 x^{2}(3 x + 1) . Grouping the last two terms and factoring out their GCF, LaTeX: \displaystyle -4 , gives LaTeX: \displaystyle -4(3 x + 1) . The polynomial now has a common binomial factor of LaTeX: \displaystyle 3 x + 1 . This gives LaTeX: \displaystyle 9 x^{2} \left(3 x + 1\right) -4 \cdot \left(3 x + 1\right) = \left(3 x + 1\right) \left(9 x^{2} - 4\right) . The quadratic factor can be factored using the difference of squares to give LaTeX: \displaystyle \left(3 x - 2\right) \left(3 x + 1\right) \left(3 x + 2\right).