### Instruction: A polynomial with integer coefficients is of the form
\[x^3 + a_2 x^2 + a_1 x - 11 = 0.\]Enter all the possible integer roots of this polynomial, separated by commas.### Response: To find the possible integer roots of this polynomial, I can use the rational root theorem, which says that any rational root of the form p/q, where p and q are coprime integers, must satisfy p being a factor of the constant term and q being a factor of the leading coefficient.
In this case, the constant term is -11 and the leading coefficient is 1, so the possible values of p are ±1, ±11 and the possible values of q are ±1.
Therefore, the possible rational roots are ±1, ±11.
However, the question only asks for the possible integer roots, which are the rational roots with q = 1.
So the possible integer roots are ±1, ±11.