Factor $LaTeX: \displaystyle 56 x^{3} + 32 x^{2} + 21 x + 12$ .

Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 8 x^{2}$ , gives $LaTeX: \displaystyle 8 x^{2}(7 x + 4)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle 3$ , gives $LaTeX: \displaystyle 3(7 x + 4)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 7 x + 4$ . This gives $LaTeX: \displaystyle 8 x^{2} \left(7 x + 4\right) +3 \cdot \left(7 x + 4\right) = \left(7 x + 4\right) \left(8 x^{2} + 3\right)$ .