Factor $LaTeX: \displaystyle - 30 x^{3} - 18 x^{2} - 35 x - 21$ .

Factoring out the GCF $LaTeX: \displaystyle -1$ from each term gives $LaTeX: \displaystyle -(30 x^{3} + 18 x^{2} + 35 x + 21)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 6 x^{2}$ , gives $LaTeX: \displaystyle 6 x^{2}(5 x + 3)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle 7$ , gives $LaTeX: \displaystyle 7(5 x + 3)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 5 x + 3$ . This gives $LaTeX: \displaystyle -1[6 x^{2} \left(5 x + 3\right) +7 \cdot \left(5 x + 3\right)] = -\left(5 x + 3\right) \left(6 x^{2} + 7\right)$ .