if the rational number x b c is a zero of the nth

Question

If the rational number x= b/ c is a zero of the n^th degree polynomial,

                                     P ( x ) = sxⁿ+ ...........+ 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.