Factor $LaTeX: \displaystyle 15 x^{3} + 10 x^{2} - 3 x - 2$ .

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