Factor $LaTeX: \displaystyle 27 x^{3} - 3 x^{2} + 45 x - 5$ .

Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 3 x^{2}$ , gives $LaTeX: \displaystyle 3 x^{2}(9 x - 1)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle 5$ , gives $LaTeX: \displaystyle 5(9 x - 1)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 9 x - 1$ . This gives $LaTeX: \displaystyle 3 x^{2} \left(9 x - 1\right) +5 \cdot \left(9 x - 1\right) = \left(9 x - 1\right) \left(3 x^{2} + 5\right)$ .