Factor $LaTeX: \displaystyle 21 x^{3} - 18 x^{2} + 35 x - 30$ .

Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 3 x^{2}$ , gives $LaTeX: \displaystyle 3 x^{2}(7 x - 6)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle 5$ , gives $LaTeX: \displaystyle 5(7 x - 6)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 7 x - 6$ . This gives $LaTeX: \displaystyle 3 x^{2} \left(7 x - 6\right) +5 \cdot \left(7 x - 6\right) = \left(7 x - 6\right) \left(3 x^{2} + 5\right)$ .