#### Answer

$-8, -4, -2, -1, 1, 2, 4, 8, -\frac{1}{2}, \frac{1}{2}$

#### Work Step by Step

RECALL:
The possible rational zeros of a polynomial function is given by $\dfrac{p}{q}$ where:
$p$ = factor of the constant term
$q$ = factor of the leading coefficient
The given polynomial function has:
constant term = $-8$
leading coefficient = $2$
The factors of the constant term are: $\pm1, \pm2, \pm 4, \pm8$
The factors of the leading coefficient are: $\pm 1, \pm2$
Thus, the possible rational zeros of the given polynomial function are:
$=\pm 1, \pm 2, \pm 4, \pm8, \pm\frac{1}{2}, \pm\frac{2}{2}, \pm \frac{4}{2}, \pm\frac{8}{2}
\\=\pm 1, \pm 2, \pm 4, \pm8, \pm\frac{1}{2}, \pm1, \pm2, \pm4
$
Eliminate the duplicates to obtain:
$\\=\pm 1, \pm 2, \pm 4, \pm8, \pm\frac{1}{2}$