Use the Rational Root Theorem to list all possible rational roots of the polynomial equation x3 – x2 – x – 3 = 0. Do not find the actual roots.

Answer 1

The Rational Root Theorem states that if a polynomial equation has a rational root r, then r is a factor of the constant term divided by a factor of the leading coefficient.

In the given polynomial equation, the constant term is -3 and the leading coefficient is 1. The factors of the constant term are ±1 and ±3, and the factors of the leading coefficient are ±1.

Therefore, the possible rational roots of the polynomial equation are:

±1/1 = ±1, ±3/1 = ±3, ±1/1 = ±1, ±3/1 = ±3

So, the possible rational roots of the equation x^3 - x^2 - x - 3 = 0 are ±1, ±3.