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.

Question

(1 point)
Responses

–3, –1, 1, 3
–3, –1, 1, 3

1, 3
1, 3

–33
–33

no roots

Answer 1

The Rational Root Theorem states that any rational root of a polynomial equation must be a factor of the constant term divided by a factor of the leading coefficient.

In this equation, the constant term is -3 and the leading coefficient is 1. Therefore, the possible rational roots are found by taking the factors of -3 (±1, ±3) and dividing them by the factors of 1 (±1).

The possible rational roots are: -3, -1, 1, 3.

So, the correct answer is: –3, –1, 1, 3.