ration root theorem

Question

Using the Rational Root Theorem, list all the possible rational roots of the polynomial.

g(x)=9x^4+3x^3+3x^2-x+27

Answer 1

Your possible rational roots are all of the factors of your constant over all the factors of your leading coefficient.

Factors of 27: 1, 3, 9, 27

Factors of 9: 1, 3, 9

So, we have 1/1, 1/3, 1/9, 3/1, 3/3, 3/9, 9/1, 9/3, 9/9, 27/1, 27/3, 27/9

All possible rational roots are: 1/3, 1/9, 1, 3, 9, 27