Factor $LaTeX: \displaystyle - 12 x^{3} + 21 x^{2} - 40 x + 70$ .

Factoring out the GCF $LaTeX: \displaystyle -1$ from each term gives $LaTeX: \displaystyle -(12 x^{3} - 21 x^{2} + 40 x - 70)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 3 x^{2}$ , gives $LaTeX: \displaystyle 3 x^{2}(4 x - 7)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle 10$ , gives $LaTeX: \displaystyle 10(4 x - 7)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 4 x - 7$ . This gives $LaTeX: \displaystyle -1[3 x^{2} \left(4 x - 7\right) +10 \cdot \left(4 x - 7\right)] = -\left(4 x - 7\right) \left(3 x^{2} + 10\right)$ .