Find all rational roots of the polynomial:?

Question

Find all rational roots of the polynomial:
P(x) = 2/3x ^6 - x ^5 - 13/3x^ 4 + 29/3x^ 3 - 9 x ^2 + 32//3x - 4 , and then find the irrational roots, if any.

a. -3, 1/2, and 2
b. -3, -1/2, and 1
c. 1, 2, and 5/2
d. 2/3, 4/3, and 2
e. -1/2, 1, and 3

Answer 1

multiply by 3 and get
2x^6-3x^5-13x^4+29x^3-27x^2+32x-12=0
if p/q is a solution p must divide 12 and q must divide 2
so d cant be as 4/3 3 does not divide 2
and c also as 5 does not divide 12
b is not as 1 is not a solution and also c and e
Having discarded b,c,d and e try a)