Factor $LaTeX: \displaystyle 30 x^{3} + 15 x^{2} - 60 x - 30$ .

Factoring out the GCF $LaTeX: \displaystyle 15$ from each term gives $LaTeX: \displaystyle 15(2 x^{3} + x^{2} - 4 x - 2)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle x^{2}$ , gives $LaTeX: \displaystyle x^{2}(2 x + 1)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -2$ , gives $LaTeX: \displaystyle -2(2 x + 1)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 2 x + 1$ . This gives $LaTeX: \displaystyle 15[x^{2} \left(2 x + 1\right) -2 \cdot \left(2 x + 1\right)] = 15\left(2 x + 1\right) \left(x^{2} - 2\right)$ .