Factor $LaTeX: \displaystyle 90 x^{3} - 40 x^{2} - 54 x + 24$ .

Factoring out the GCF $LaTeX: \displaystyle 2$ from each term gives $LaTeX: \displaystyle 2(45 x^{3} - 20 x^{2} - 27 x + 12)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 5 x^{2}$ , gives $LaTeX: \displaystyle 5 x^{2}(9 x - 4)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -3$ , gives $LaTeX: \displaystyle -3(9 x - 4)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 9 x - 4$ . This gives $LaTeX: \displaystyle 2[5 x^{2} \left(9 x - 4\right) -3 \cdot \left(9 x - 4\right)] = 2\left(9 x - 4\right) \left(5 x^{2} - 3\right)$ .