f(x) = 3x⁵ - 7x³ + 2x - 15

List all the factors of 15, the number on the right end 
of the right side, ignoring the sign for the time being:
They are

1, 3, 5, 15

List all the factors of 3, the coefficient of of x⁵, also
ignoring the sign for the time being:

1, 3

Now make every possible fraction you can make taking the 
numerator from 1, 3, 5, 15  and the denominator from 1, 3

1/1, 1/3, 3/1, 3/3, 5/1, 5/3, 15/1, 15/3

Simplify them:

1, 1/3, 3, 1, 5, 5/3, 15, 5

Throw out the duplicates:

1, 1/3, 3, 5, 5/3, 15

Now put ± in front of each:

±1, ±1/3, ±3, ±5, ±5/3, ±15

That's it!

Edwin