If the rational number x= b/ c is a zero of the n^{th} degree polynomial,
P ( x ) = sx^{n}+ ...........+ t
Where every the coefficients are integers then b will be a factor of t & c will be a factor of s.
Note that in order for this theorem to work then the zero have to be reduced to lowest terms. In other terms it will work for 4/3 but not necessarily for 20/15.