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

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