### Instruction: A polynomial with integer coefficients is of the form
\[3x^3 + a_2 x^2 + a_1 x - 6 = 0.\]Enter all the possible integer roots of this polynomial, separated by commas.### Response: To find the possible integer roots of a polynomial with integer coefficients, I can use the rational root theorem.
This theorem says that if p/q is a rational root of the polynomial, then p must be a factor of the constant term and q must be a factor of the leading coefficient.
In this case, the constant term is -6 and the leading coefficient is 3.
The factors of -6 are $\pm 1, \pm 2, \pm 3, \pm 6$, and the factors of 3 are $\pm 1, \pm 3$.
Therefore, the possible rational roots are $\pm 1, \pm 2, \pm 3, \pm 6, \pm \frac{1}{3}, \pm \frac{2}{3}, \pm \frac{6}{3}$.
But I only want the integer roots, so I can ignore the fractions.
The possible integer roots are $\pm 1, \pm 2, \pm 3, \pm 6$.