Factor $LaTeX: \displaystyle - 10 x^{3} - 45 x^{2} - 12 x - 54$ .

Factoring out the GCF $LaTeX: \displaystyle -1$ from each term gives $LaTeX: \displaystyle -(10 x^{3} + 45 x^{2} + 12 x + 54)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 5 x^{2}$ , gives $LaTeX: \displaystyle 5 x^{2}(2 x + 9)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle 6$ , gives $LaTeX: \displaystyle 6(2 x + 9)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 2 x + 9$ . This gives $LaTeX: \displaystyle -1[5 x^{2} \left(2 x + 9\right) +6 \cdot \left(2 x + 9\right)] = -\left(2 x + 9\right) \left(5 x^{2} + 6\right)$ .