The theorem is used in order to determine whether a polynomial has any rational roots, and if so to find them. Since the theorem gives constraints on the numerator and denominator of the fully reduced rational roots as being divisors of certain numbers, all possible combinations of divisors can be checked and either the rational roots will be found or it will be determined that there rational numbers test pdf none.
If one or more are found, they can be factored out of the polynomial, resulting in a polynomial of lower degree whose roots are also roots of the original polynomial. But if the test finds three rational solutions, then the cube roots are avoided. 1 and a denominator that divides evenly into 2. 3 equate the polynomial to zero, and hence are its rational roots. In this particular case there is exactly one rational root.