Factor $LaTeX: \displaystyle - 20 x^{3} + 10 x^{2} - 90 x + 45$ .

Factoring out the GCF $LaTeX: \displaystyle -5$ from each term gives $LaTeX: \displaystyle -5(4 x^{3} - 2 x^{2} + 18 x - 9)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 2 x^{2}$ , gives $LaTeX: \displaystyle 2 x^{2}(2 x - 1)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle 9$ , gives $LaTeX: \displaystyle 9(2 x - 1)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 2 x - 1$ . This gives $LaTeX: \displaystyle -5[2 x^{2} \left(2 x - 1\right) +9 \cdot \left(2 x - 1\right)] = -5\left(2 x - 1\right) \left(2 x^{2} + 9\right)$ .