Factor $LaTeX: \displaystyle 21 x^{3} + 27 x^{2} + 70 x + 90$ .

Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 3 x^{2}$ , gives $LaTeX: \displaystyle 3 x^{2}(7 x + 9)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle 10$ , gives $LaTeX: \displaystyle 10(7 x + 9)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 7 x + 9$ . This gives $LaTeX: \displaystyle 3 x^{2} \left(7 x + 9\right) +10 \cdot \left(7 x + 9\right) = \left(7 x + 9\right) \left(3 x^{2} + 10\right)$ .