Factor $LaTeX: \displaystyle - 60 x^{3} + 18 x^{2} + 90 x - 27$ .

Factoring out the GCF $LaTeX: \displaystyle -3$ from each term gives $LaTeX: \displaystyle -3(20 x^{3} - 6 x^{2} - 30 x + 9)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 2 x^{2}$ , gives $LaTeX: \displaystyle 2 x^{2}(10 x - 3)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -3$ , gives $LaTeX: \displaystyle -3(10 x - 3)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 10 x - 3$ . This gives $LaTeX: \displaystyle -3[2 x^{2} \left(10 x - 3\right) -3 \cdot \left(10 x - 3\right)] = -3\left(10 x - 3\right) \left(2 x^{2} - 3\right)$ .