Consider $2x^{3}-3x^{2}-12x+18$. Do the grouping $2x^{3}-3x^{2}-12x+18=\left(2x^{3}-3x^{2}\right)+\left(-12x+18\right)$, and factor out $x^{2}$ in the first and $-6$ in the second group.
$$x^{2}\left(2x-3\right)-6\left(2x-3\right)$$
Factor out common term $2x-3$ by using distributive property.
$$\left(2x-3\right)\left(x^{2}-6\right)$$
Rewrite the complete factored expression. Polynomial $x^{2}-6$ is not factored since it does not have any rational roots.
