Answer
$\pm1, \pm2, \pm5,\pm 10$
Work Step by Step
Given: $f(x)=2x^4+6x^3-7x+9$
Factors of the constant term: $\pm 1, \pm 2, \pm 5, \pm 10$
Factors of the leading coefficient: $\pm 1$
Possible rational zeros: $\pm \frac{1}{1}, \pm \frac{2}{1}, \pm \frac{5}{1}, \pm \frac{10}{1}$
Simplified list of possible zeros: $\pm1, \pm2, \pm5,\pm 10$
