use the rational root theorem to list all possible rational roots of the polynomial equation x^3-x^2-x-3=0. do not find actual roots
The Rational Root Theorem states that if a polynomial equation has a rational root, it must be of the form p/q, where p is a factor of the constant term (in this case, 3) and q is a factor of the leading coefficient (in this case, 1).
The factors of 3 are ±1 and ±3, and the factors of 1 are ±1. Therefore, the possible rational roots of the polynomial equation x^3 - x^2 - x - 3 = 0 are:
±1, ±3.