Answer
$\displaystyle \pm 1,\pm\frac{1}{2},\pm\frac{1}{3},\pm\frac{1}{6},\pm 2,\pm\frac{2}{3},\pm 5,\pm\frac{5}{2}\pm\frac{5}{3},\pm\frac{5}{6},\pm 10,\pm\frac{10}{3}$
Work Step by Step
Rational Zeros Theorem:
Let $f$ be a polynomial function of degree 1 or higher of the form
$f(x)=a_{n}x^{n}+a_{n-1}x^{n-1}+\cdots+a_{1}x+a_{0},\quad a_{n}\neq 0,\quad a_{0}\neq 0$
where each coefficient is an integer.
If $\displaystyle \frac{p}{q},$ in lowest terms, is a rational zero of $f,$ then $p$ must be a factor of $a_{0},$
and $q$ must be a factor of $a_{n}$ .
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possible p: $\pm 1,\pm 2,\pm 5,\pm 10$
possible q: $\pm 1,\pm 2,\pm 3,+6$
possible rational roots $\displaystyle \frac{p}{q}$ :
$\displaystyle \pm 1,\pm\frac{1}{2},\pm\frac{1}{3},\pm\frac{1}{6},\pm 2,\pm\frac{2}{3},\pm 5,\pm\frac{5}{2}\pm\frac{5}{3},\pm\frac{5}{6},\pm 10,\pm\frac{10}{3}$
