Factor $LaTeX: \displaystyle - 2 x^{3} + 8 x^{2} + 18 x - 72$ .

Factoring out the GCF $LaTeX: \displaystyle -2$ from each term gives $LaTeX: \displaystyle -2(x^{3} - 4 x^{2} - 9 x + 36)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle x^{2}$ , gives $LaTeX: \displaystyle x^{2}(x - 4)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -9$ , gives $LaTeX: \displaystyle -9(x - 4)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle x - 4$ . This gives $LaTeX: \displaystyle -2[x^{2} \left(x - 4\right) -9 \cdot \left(x - 4\right)] = -2\left(x - 4\right) \left(x^{2} - 9\right)$ . The quadratic factor can be factored using the difference of squares to give $LaTeX: \displaystyle -2\left(x - 4\right) \left(x - 3\right) \left(x + 3\right).$