Answer
$\pm1, \pm2, \pm4,\pm 7, \pm14, \pm 28$
Work Step by Step
Given: $f(x)=x^3-3x+28$
Factors of the constant term: $\pm 1, \pm 2, \pm 4, \pm 7, \pm 14, \pm 28$
Factors of the leading coefficient: $\pm 1$
Possible rational zeros: $\pm \frac{1}{1}, \pm \frac{2}{1}, \pm \frac{4}{1}, \pm \frac{7}{1}, \pm \frac{14}{1}, \pm \frac{28}{1}$
Simplified list of possible zeros: $\pm1, \pm2, \pm4,\pm 7, \pm14, \pm 28$
