Question 886915
<pre>
{{{"P(x)"}}}{{{""=""}}}{{{3x^3 -4x^2 +7x -10}}}.

The factors of the absolute value of the constant term,
-10, (which is |-10| or 10):

{{{matrix(1,8,1,",", 2,",", 5,",", and, 10)}}}

The factors of the absolute value of the coefficient of the 
leading term, 3, the term with the largest exponent,
which is |3| or 3: 

{{{matrix(1,4,1,",", and, 3)}}}
 
Now we make all the fractions possible using one of these 
1, 2, 5, and 10 as the numerator and one of these 1 and 3
as the denominator:

{{{matrix(1,15,1/1,",", 1/3,",", 2/1,",", 2/3,",", 5/1,",", 5/3,",", 10/1,",", 10/3)}}}

Reduce any of them if possible:

{{{matrix(1,15,1,",", 1/3,",", 2,",", 2/3,",", 5,",", 5/3,",", 10,",", 10/3)}}}

Put ± in front of each:

{{{matrix(1,15,
"" +- 1,
",",
"" +- 1/3,
",",
"" +- 2,
",",
"" +- 2/3,
",",
"" +- 5,
",",
"" +- 5/3,
",",
"" +- 10,
",",
 "" +- 10/3
)}}}

That's the list of all candidates for rational solutions.

Edwin</pre>