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

Factoring out the GCF $LaTeX: \displaystyle -1$ from each term gives $LaTeX: \displaystyle -(3 x^{3} + 2 x^{2} - 27 x - 18)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle x^{2}$ , gives $LaTeX: \displaystyle x^{2}(3 x + 2)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -9$ , gives $LaTeX: \displaystyle -9(3 x + 2)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 3 x + 2$ . This gives $LaTeX: \displaystyle -1[x^{2} \left(3 x + 2\right) -9 \cdot \left(3 x + 2\right)] = -\left(3 x + 2\right) \left(x^{2} - 9\right)$ . The quadratic factor can be factored using the difference of squares to give $LaTeX: \displaystyle -\left(x - 3\right) \left(x + 3\right) \left(3 x + 2\right).$