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

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