If the coefficients of the polynomial
 |
(1)
|
are specified to be integers, then rational roots must have a numerator which is a factor of 
and a denominator which
is a factor of 
(with either sign possible). This follows since a polynomial
of polynomial order 
with 
rational roots can be expressed as
 |
(2)
|
where the roots are 
, 
, ..., and 
. Factoring out the 
s,
 |
(3)
|
Now, multiplying through,
 |
(4)
|
where we have not bothered with the other terms. Since the first and last coefficients are 
and 
,
all the rational roots of equation (1) are of the form
[factors of 
]/[factors
of 
].
