Factor $LaTeX: \displaystyle - 14 x^{3} + 8 x^{2} + 14 x - 8$ .

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