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 the actual roots
-3,-1,1,3
1,3
-33
no roots
The Rational Root Theorem states that if a polynomial equation has a rational root p/q, where p and q are integers with no common factors (other than 1) and q is not zero, then p must be a factor of the constant term of the polynomial and q must be a factor of the leading coefficient.
In the given equation, the constant term is -3 and the leading coefficient is 1. The factors of -3 are ±1 and ±3, and the factors of 1 are ±1. Therefore, the possible rational roots are:
±1/±1 (which simplifies to ±1)
±3/±1 (which simplifies to ±3)
So, the possible rational roots are: -3, -1, 1, 3.