Factor $LaTeX: \displaystyle - 54 x^{3} - 36 x^{2} - 90 x - 60$ .

Factoring out the GCF $LaTeX: \displaystyle -6$ from each term gives $LaTeX: \displaystyle -6(9 x^{3} + 6 x^{2} + 15 x + 10)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 3 x^{2}$ , gives $LaTeX: \displaystyle 3 x^{2}(3 x + 2)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle 5$ , gives $LaTeX: \displaystyle 5(3 x + 2)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 3 x + 2$ . This gives $LaTeX: \displaystyle -6[3 x^{2} \left(3 x + 2\right) +5 \cdot \left(3 x + 2\right)] = -6\left(3 x + 2\right) \left(3 x^{2} + 5\right)$ .