Factor $LaTeX: \displaystyle - 25 x^{3} - 10 x^{2} + 30 x + 12$ .

Factoring out the GCF $LaTeX: \displaystyle -1$ from each term gives $LaTeX: \displaystyle -(25 x^{3} + 10 x^{2} - 30 x - 12)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 5 x^{2}$ , gives $LaTeX: \displaystyle 5 x^{2}(5 x + 2)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -6$ , gives $LaTeX: \displaystyle -6(5 x + 2)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 5 x + 2$ . This gives $LaTeX: \displaystyle -1[5 x^{2} \left(5 x + 2\right) -6 \cdot \left(5 x + 2\right)] = -\left(5 x + 2\right) \left(5 x^{2} - 6\right)$ .