Given a polynomial with integer coefficients:

How to make a list of numbers such that if there are any rational zeros
for a polynomial, they will all be in the list of numbers.

1.  Find all possible factors of the absolute value of the coefficient of the 
    nonzero term with LEAST degree. 

2.  Find all possible factors of the absolute value of the coefficient of the 
    nonzero term with GREATEST degree. 

3.  List all possible fractions whose numerator is in the first list and
    whose denominator is in the second list.

4.  Also include all the negatives of those fractions.


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1.  All the factor of 6 are 1,2,3,6

2.  All the factors of 2 are 1 and 2

3.  All the fractions are 1/1, 1/2, 2/1, 2/2, 3/1, 3/2, 6/1, 6/2

Reducting the reducible ones:

                            1, 1/2, 2, 1, 3, 3/2, 6, 3

Toss out the dupicates:     1, 1/2, 2, 3, 3/2, 6

4.  Also include their negatives (opposites:

                           ±1, ±1/2, ±2, ±3, ±3/2, ±6

If there are any rational zeros of 2x^3-4x^2+5x+6, they will be in
that list.

As it turns out, unfortunately, none of those are zeros of  f(x)=2x^3-4x^2+5x+6.

[This proves that the word "possible", although all teachers and textbooks use
that word, that is the wrong word to use because, for example, in this case none
of them are really 'possible rational zeros'.]

Edwin