Factor $LaTeX: \displaystyle 54 x^{3} + 12 x^{2} + 36 x + 8$ .

Factoring out the GCF $LaTeX: \displaystyle 2$ from each term gives $LaTeX: \displaystyle 2(27 x^{3} + 6 x^{2} + 18 x + 4)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 3 x^{2}$ , gives $LaTeX: \displaystyle 3 x^{2}(9 x + 2)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle 2$ , gives $LaTeX: \displaystyle 2(9 x + 2)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 9 x + 2$ . This gives $LaTeX: \displaystyle 2[3 x^{2} \left(9 x + 2\right) +2 \cdot \left(9 x + 2\right)] = 2\left(9 x + 2\right) \left(3 x^{2} + 2\right)$ .