Factor $LaTeX: \displaystyle 6 x^{3} - 9 x^{2} + 14 x - 21$ .

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