Question

50 pts. & will give brainliest! 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. (1 point)
a. -3, -1, 1, 3
b. 1, 3
c. -3, 3
d. no roots

Answer 1

Answer:

The Cubic Polynomial given here is

x³ - x² - x -3 =0

Rational root theorem :

Consider any polynomial

$→ Ax^n +A_{1}x^{n-1}+A_{2}x^{n-2}+.................+A_{n}=0Axn+A1xn−1+A2xn−2+.................+An=0$

So, the factors of this polynomial is those number which divides An/A which are ±1, An/A.

Applying the same method the number which divides (-3) are,-3,+3,-1,+1. So By rational root theorem all the factors of this cubic polynomial is 3,±1,±3 .

Option 1. -3,-1,1,3 is correct option