Factor $LaTeX: \displaystyle - 12 x^{3} + 6 x^{2} - 42 x + 21$ .

Factoring out the GCF $LaTeX: \displaystyle -3$ from each term gives $LaTeX: \displaystyle -3(4 x^{3} - 2 x^{2} + 14 x - 7)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 2 x^{2}$ , gives $LaTeX: \displaystyle 2 x^{2}(2 x - 1)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle 7$ , gives $LaTeX: \displaystyle 7(2 x - 1)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 2 x - 1$ . This gives $LaTeX: \displaystyle -3[2 x^{2} \left(2 x - 1\right) +7 \cdot \left(2 x - 1\right)] = -3\left(2 x - 1\right) \left(2 x^{2} + 7\right)$ .