Question 764422
The question basically asks to determine the list of all possible rational root values to test or check for.


You would have in general, something like {{{y=ax^3+bx^2+cx+d}}}.
All possible factors of 'a' give the individual values of q to use in p/q;
All possible factors of d give the individual values of p to use in p/q.


Check you polynomial in general form, and completely factor, or find all possible factors of a.  Find all possible factors of d.
Now, form ALL possible rational numbers using your lists of p and q.  


Your example is {{{ f(x)=x(x^3-4x^2-7x+28)}}}, assuming you forgot to put the exponent on one of your terms.

Your 'a' is a=1, so the only factor is 1.
Your d is d=28, and its factors are PLUS AND MINUS 1, 2, 4, 7, 14, 28.

Your possible rational values to check about roots for f(x) are the values p/q from the list PLUS AND MINUS of 1, 2, 4, 7, 14, 28.
Since you are told to give your answer in factored form, you want to say, 
{{{-1/1}}}, {{{-1/2}}}, {{{-1/4}}}, {{{-1/7}}}, {{{-1/14}}}, {{{-1/28}}}, {{{1/1}}}, {{{1/2}}}, {{{1/4}}}, {{{1/7}}}, {{{1/14}}}, {{{1/28}}}