Use the rational root theorem to list all possible rational roots for the equation.
3x^3+9x-6=0

Step-by-step explanation:

The given expression is

The rational root theorem states the divisors of the constant are possible roots. Additionally, if the term with the greater exponent as a coefficient different than one, then we must incluce its divisor, to then divide them by the divisor of the constant.

According to the theorem, all possible rational roots are

Divisors of 6: 1, 2, 3, 6.

Divisors of 3: 1, 3.

Possible rational roots: 1/1, 1/3, 2/1, 2/3, 3/1, 3/3, 6/1, 6/3.

Therefore, all possible rational roots are: 1, 1/3, 2, 2/3, 3, 6.