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

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