Factor $LaTeX: \displaystyle - 16 x^{3} + 16 x^{2} + 8 x - 8$ .

Factoring out the GCF $LaTeX: \displaystyle -8$ from each term gives $LaTeX: \displaystyle -8(2 x^{3} - 2 x^{2} - x + 1)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 2 x^{2}$ , gives $LaTeX: \displaystyle 2 x^{2}(x - 1)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -1$ , gives $LaTeX: \displaystyle -1(x - 1)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle x - 1$ . This gives $LaTeX: \displaystyle -8[2 x^{2} \left(x - 1\right) -1 \cdot \left(x - 1\right)] = -8\left(x - 1\right) \left(2 x^{2} - 1\right)$ .