Answer
$\pm 1, \pm 2, \pm4, \pm8, \pm\frac{1}{2}, \pm\frac{1}{3}, \pm\frac{1}{4}, \pm\frac{1}{6}, \pm\frac{1}{12}, \pm\frac{2}{3},\pm\frac{4}{3}, \pm\frac{8}{3}$
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 = $12$
The factors of the constant term are: $\pm1, \pm2, \pm4, \pm8$
The factors of the leading coefficient are: $\pm 1, \pm2, \pm3, \pm4, \pm6, \pm12$
Thus, the possible rational zeros of the given polynomial function are:
$\pm 1, \pm 2, \pm4, \pm8, \pm\frac{1}{2}, \pm\frac{1}{3}, \pm\frac{1}{4}, \pm\frac{1}{6}, \pm\frac{1}{12}, \pm\frac{2}{3},\pm\frac{4}{3}, \pm\frac{8}{3}$
