Factor $LaTeX: \displaystyle 2 x^{3} - 9 x^{2} - 10 x + 45$ .

Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle x^{2}$ , gives $LaTeX: \displaystyle x^{2}(2 x - 9)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -5$ , gives $LaTeX: \displaystyle -5(2 x - 9)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 2 x - 9$ . This gives $LaTeX: \displaystyle x^{2} \left(2 x - 9\right) -5 \cdot \left(2 x - 9\right) = \left(2 x - 9\right) \left(x^{2} - 5\right)$ .