* The Rational Root Theorem says if a polynomial equation has rational root then the denominator q divides the leading coefficient and the numerator p divides *.

As an addition to this theorem, for every whole number k, number p – kq is a divisor of f(k).

Example 1. Find all rational roots of the following equation:

The leading coefficient is 5 which means that, since q divides it, is from the set {-1, 1, -5, 5} and the free coefficient is number 3 which means that p is from the set {-1, 1, -3, 3}.

Since we know possibilities for q and p, we can find all combinations to see what our solutions, can be.

The first solution is 1. When we factorize given equation we get:

Since the other factor is a quadratic polynomial, we can easily find its roots. As the final result we get: