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

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