Answer
Possible rational roots: $\pm \frac{1}{3}$, $\pm \frac{2}{3}$, $\pm 1$, $\pm \frac{4}{3}$, $\pm 2$, , $\pm 3$, $\pm 4$, $\pm 6$, $\pm 12$
Work Step by Step
The coefficient of the leading term is $3$, and the constant is $-12$.
Find the factors of the coefficient of the leading term and the factors of the constant term:
Coefficient of the leading term factors:
$\pm 1$, $\pm 3$
Constant term factors:
$\pm 1$, $\pm 12$, $\pm 6$, $\pm 2$, $\pm 4$, $\pm 3$
Possible rational roots can be found using the formula:
$\frac{p}{q}$, where $p$ is a factor of the constant term and $q$ is a factor of the leading coefficient.
Plug factors into this formula:
Possible rational roots: $\pm \frac{1}{1}$, $\pm \frac{1}{3}$, $\pm \frac{12}{1}$, $\pm \frac{12}{3}$, $\pm \frac{6}{1}$, $\pm \frac{6}{3}$, $\pm \frac{2}{1}$, $\pm \frac{2}{3}$, $\pm \frac{4}{1}$, $\pm \frac{4}{3}$, $\pm \frac{3}{1}$, $\pm \frac{3}{3}$
Simplify the fractions, leaving out duplicate roots:
Possible rational roots: $\pm 1$, $\pm \frac{1}{3}$, $\pm 12$, $\pm 4$, $\pm 6$, $\pm 2$, $\pm \frac{2}{3}$, $\pm \frac{4}{3}$, $\pm 3$
