Factor $LaTeX: \displaystyle 6 x^{3} - 14 x^{2} - 3 x + 7$ .

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