Factor $LaTeX: \displaystyle - 12 x^{3} + 14 x^{2} + 30 x - 35$ .

Factoring out the GCF $LaTeX: \displaystyle -1$ from each term gives $LaTeX: \displaystyle -(12 x^{3} - 14 x^{2} - 30 x + 35)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 2 x^{2}$ , gives $LaTeX: \displaystyle 2 x^{2}(6 x - 7)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -5$ , gives $LaTeX: \displaystyle -5(6 x - 7)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 6 x - 7$ . This gives $LaTeX: \displaystyle -1[2 x^{2} \left(6 x - 7\right) -5 \cdot \left(6 x - 7\right)] = -\left(6 x - 7\right) \left(2 x^{2} - 5\right)$ .