Factor $LaTeX: \displaystyle - 32 x^{3} + 32 x^{2} - 12 x + 12$ .

Factoring out the GCF $LaTeX: \displaystyle -4$ from each term gives $LaTeX: \displaystyle -4(8 x^{3} - 8 x^{2} + 3 x - 3)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 8 x^{2}$ , gives $LaTeX: \displaystyle 8 x^{2}(x - 1)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle 3$ , gives $LaTeX: \displaystyle 3(x - 1)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle x - 1$ . This gives $LaTeX: \displaystyle -4[8 x^{2} \left(x - 1\right) +3 \cdot \left(x - 1\right)] = -4\left(x - 1\right) \left(8 x^{2} + 3\right)$ .