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

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