Factor $LaTeX: \displaystyle - 18 x^{3} - 90 x^{2} + 8 x + 40$ .

Factoring out the GCF $LaTeX: \displaystyle -2$ from each term gives $LaTeX: \displaystyle -2(9 x^{3} + 45 x^{2} - 4 x - 20)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 9 x^{2}$ , gives $LaTeX: \displaystyle 9 x^{2}(x + 5)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -4$ , gives $LaTeX: \displaystyle -4(x + 5)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle x + 5$ . This gives $LaTeX: \displaystyle -2[9 x^{2} \left(x + 5\right) -4 \cdot \left(x + 5\right)] = -2\left(x + 5\right) \left(9 x^{2} - 4\right)$ . The quadratic factor can be factored using the difference of squares to give $LaTeX: \displaystyle -2\left(x + 5\right) \left(3 x - 2\right) \left(3 x + 2\right).$