Factor LaTeX: \displaystyle - 54 x^{3} + 30 x^{2} + 54 x - 30 .

Factoring out the GCF LaTeX: \displaystyle -6 from each term gives LaTeX: \displaystyle -6(9 x^{3} - 5 x^{2} - 9 x + 5) . Grouping the first two terms and factoring out their GCF, LaTeX: \displaystyle x^{2} , gives LaTeX: \displaystyle x^{2}(9 x - 5) . Grouping the last two terms and factoring out their GCF, LaTeX: \displaystyle -1 , gives LaTeX: \displaystyle -1(9 x - 5) . The polynomial now has a common binomial factor of LaTeX: \displaystyle 9 x - 5 . This gives LaTeX: \displaystyle -6[x^{2} \left(9 x - 5\right) -1 \cdot \left(9 x - 5\right)] = -6\left(9 x - 5\right) \left(x^{2} - 1\right) . The quadratic factor can be factored using the difference of squares to give LaTeX: \displaystyle -6\left(x - 1\right) \left(x + 1\right) \left(9 x - 5\right).