List all the possible rational solutions of 3x^4-2x^3+11x-1=0.

Answer 1

±1, ±1/3 from the rational roots theorem

Answer 2

all the multiples of p (-1) over all the multiples of q (3) yeild the only four possible rational solutions:

±1

---- or

±1

±1

----

±3

so the four possible are -1, -1/3, 1, 1/3

Using synthetic division (looking for a remainder of 0) we find that none of these possible rational solutions result in actual solutions.

Here is a helpful example on this webpage

https://www.sparknotes.com/math/algebra2/polynomials/section4/