How do you find all the rational zeros of a polynomial function?
You can use the rational root theorem:
Given a polynomial of the form:
all rational roots of the form
This gives you a finite number of possible rational roots to try.
For example, the rational roots of
must be of the form
You can try substituting each of the possible combinations of
In fact the only rational roots it has are
Once you have found one root, you can divide the polynomial by the corresponding factor to simplify the problem.