Use the rational root theorem to list all possible rational roots for the equation 3x³ + 9x - 6 = 0.

Solution:

Given, the equation is 3x³ + 9x - 6 = 0

We have to find the roots of the equation by rational root theorem.

By rational root theorem,

Rational roots = factors of constant term/factors of leading coefficient

The factors of constant term 6 are 1, 2, 3, 6.

The factors of leading coefficient 3 are 1, 3.

So, roots = ±(1, 2, 3, 6)/(1,3)

Therefore, the possible rational roots are ±1, ±2, ±1/3, ±2/3, ±3, ±6.

Use the rational root theorem to list all possible rational roots for the equation 3x³ + 9x - 6 = 0.

Summary:

Using the rational root theorem, all possible rational roots for the equation 3x³ + 9x - 6 = 0 are ±1, ±2, ±1/3, ±2/3, ±3, ±6.