.

The factors of the absolute value of the constant term,
-10, (which is |-10| or 10):



The factors of the absolute value of the coefficient of the 
leading term, 3, the term with the largest exponent,
which is |3| or 3: 


 
Now we make all the fractions possible using one of these 
1, 2, 5, and 10 as the numerator and one of these 1 and 3
as the denominator:



Reduce any of them if possible:



Put ± in front of each:



That's the list of all candidates for rational solutions.

Edwin