Factor $LaTeX: \displaystyle - 4 x^{3} - 12 x^{2} - 18 x - 54$ .

Factoring out the GCF $LaTeX: \displaystyle -2$ from each term gives $LaTeX: \displaystyle -2(2 x^{3} + 6 x^{2} + 9 x + 27)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 2 x^{2}$ , gives $LaTeX: \displaystyle 2 x^{2}(x + 3)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle 9$ , gives $LaTeX: \displaystyle 9(x + 3)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle x + 3$ . This gives $LaTeX: \displaystyle -2[2 x^{2} \left(x + 3\right) +9 \cdot \left(x + 3\right)] = -2\left(x + 3\right) \left(2 x^{2} + 9\right)$ .