Factor $LaTeX: \displaystyle - 12 x^{3} + 14 x^{2} - 24 x + 28$ .

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