Factor $LaTeX: \displaystyle 3 x^{3} + 18 x^{2} - 5 x - 30$ .

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