how to use the rational zero theorem

Question

use the rational zeros theorem to list the potential rational zeros of the polynomial function.Do not attempt to find the zeros

f(x)=2x^5-x^3+2x^2-4x-8=0

Answer 1

We need the coefficients of the highest power of x and the constant:

So we have 2 and 8 (ignore the signs).

Now list all the factors of each:

2: factors 1, 2 (set Q)

8: factors 1, 2, 4, 8 (set P)

Now make up all possible fractions p/q for all p in P and q in Q, without duplicates:

1, ½, 2, 4. There are eight, because we have to include positive and negative versions of these numbers. These are the rational zeroes. To find out which (if any) are actual zeroes requires us to use synthetic division (or other means) to divide each into the polynomial.