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

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