SOLUTION: i'm still very confused on how to do this, especially getting the p/q list. can you help with this problem please? this is with the RATIONAL ROOT THEOREM find all zeros of f(x)

Question 764422: i'm still very confused on how to do this, especially getting the p/q list. can you help with this problem please? this is with the RATIONAL ROOT THEOREM
find all zeros of f(x)
f(x)=x^4-4x^3-7x+28x
Hint: first factor out an x, then get the p/q list
keep answers in fractional form.
help me please! i don't fully understand this

Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
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 .
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 , 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,
, , , , , , , , , , ,
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