Factor $LaTeX: \displaystyle - 40 x^{3} - 45 x^{2} + 32 x + 36$ .

Factoring out the GCF $LaTeX: \displaystyle -1$ from each term gives $LaTeX: \displaystyle -(40 x^{3} + 45 x^{2} - 32 x - 36)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 5 x^{2}$ , gives $LaTeX: \displaystyle 5 x^{2}(8 x + 9)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -4$ , gives $LaTeX: \displaystyle -4(8 x + 9)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 8 x + 9$ . This gives $LaTeX: \displaystyle -1[5 x^{2} \left(8 x + 9\right) -4 \cdot \left(8 x + 9\right)] = -\left(8 x + 9\right) \left(5 x^{2} - 4\right)$ .