### Instruction: A polynomial with integer coefficients is of the form
\[x^4 + a_3 x^3 + a_2 x^2 + a_1 x + 4 = 0.\]Enter all the possible integer roots of this polynomial, separated by commas.### Response: To find the possible integer roots of a polynomial, I can use the rational root theorem, which says that any rational root p/q 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 4 and the leading coefficient is 1, so p must be a factor of 4 and q must be a factor of 1.
This means that the possible rational roots are \[\pm 1, \pm 2, \pm 4.\]
These are also the possible integer roots, since q is always 1.
I could also check if any of these roots actually work by plugging them into the polynomial and seeing if it equals zero, but that is not necessary for this question.