Answer
$\pm1, \pm2, \pm3,\pm 6, \pm 9, \pm 8,\pm \frac{1}{2}, \pm \frac{3}{2},\pm \frac{9}{2}$
Work Step by Step
Given: $f(x)=2x^3+x^2-x-18$
Factors of the constant term: $\pm 1, \pm 2, \pm 3, \pm 6, \pm 9, \pm 18$
Factors of the leading coefficient: $\pm 1, \pm 2$
Possible rational zeros: $\pm \frac{1}{1}, \pm \frac{2}{1}, \pm \frac{3}{1}, \pm \frac{6}{1}, \pm \frac{9}{1}, \pm \frac{18}{1}, \pm \frac{1}{2}, \pm \frac{2}{2}, \pm \frac{3}{2}, \pm \frac{6}{2}, \pm \frac{9}{2}, \pm \frac{18}{2}$
Simplified list of possible zeros: $\pm1, \pm2, \pm3,\pm 6, \pm 9, \pm 8,\pm \frac{1}{2}, \pm \frac{3}{2},\pm \frac{9}{2}$
