Factor $LaTeX: \displaystyle - 6 x^{3} + 6 x^{2} + 7 x - 7$ .

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