Answer
$a.\displaystyle \quad\pm 1,\pm 2,\pm\frac{1}{3},\pm\frac{2}{3}$
$b.\quad-1$ and $\displaystyle \frac{2}{3}$
Work Step by Step
Rational Zeros Theorem$:$
$ ... $every rational zero of $P(x)$ is of the form $\displaystyle \frac{p}{q}$
where $p$ and $q$ are integers and
$p$ is a factor of the constant coefficient $a_{0}$
$q$ is a factor of the leading coefficient $a_{n}$
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$a.$
$P(x)=3x^{3}+4x^{2}-x-2$
candidates for p: $\pm 1,\pm 2$
candidates for q: $\pm 1,\pm 3$
Possible rational zeros $\displaystyle \frac{p}{q}$:$\displaystyle \quad \pm 1,\pm 2,\pm\frac{1}{3},\pm\frac{2}{3}$
$b.$
From the graph, the actual zeros are $-1$ and $\displaystyle \frac{2}{3}$
