# How do you find all the rational zeros of a polynomial function?

##### 1 Answer

You can use the rational root theorem:

Given a polynomial of the form:

all rational roots of the form

That is

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.