Answer
$-1, 1, -7, 7, -\frac{1}{2}, \frac{1}{2}, -\frac{1}{4}, \frac{1}{4}, -\frac{7}{2}, \frac{7}{2}, -\frac{7}{4}. \frac{7}{4}$
Work Step by Step
Note that:
The factors of $-7$ are $\pm1, \pm7$.
The factors of $4$ are $\pm1, \pm2, \pm4$
Thus,
The possible values of $p$ are $\pm1, \pm7$.
The possible values of $q$ are $\pm1, \pm2, \pm4$
Therefore the possible rational zeros $\frac{p}{q}$ of $R(x)$ are:
$\\-1, 1, -7, 7, -\frac{1}{2}, \frac{1}{2}, -\frac{1}{4}, \frac{1}{4}, -\frac{7}{2}, \frac{7}{2}, -\frac{7}{4}. \frac{7}{4}$
