Factor $LaTeX: \displaystyle 7 x^{3} - 8 x^{2} + 14 x - 16$ .

Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle x^{2}$ , gives $LaTeX: \displaystyle x^{2}(7 x - 8)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle 2$ , gives $LaTeX: \displaystyle 2(7 x - 8)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 7 x - 8$ . This gives $LaTeX: \displaystyle x^{2} \left(7 x - 8\right) +2 \cdot \left(7 x - 8\right) = \left(7 x - 8\right) \left(x^{2} + 2\right)$ .