Factor $LaTeX: \displaystyle - 18 x^{3} + 45 x^{2} - 6 x + 15$ .

Factoring out the GCF $LaTeX: \displaystyle -3$ from each term gives $LaTeX: \displaystyle -3(6 x^{3} - 15 x^{2} + 2 x - 5)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 3 x^{2}$ , gives $LaTeX: \displaystyle 3 x^{2}(2 x - 5)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle 1$ , gives $LaTeX: \displaystyle 1(2 x - 5)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 2 x - 5$ . This gives $LaTeX: \displaystyle -3[3 x^{2} \left(2 x - 5\right) +1 \cdot \left(2 x - 5\right)] = -3\left(2 x - 5\right) \left(3 x^{2} + 1\right)$ .