The equation x^3+6x^2-x-10 = 0 is the same as 1x^3+6x^2-x-10 = 0 The first term is 1x^3 and the last term is -10 Pull away the coefficient of the first term and it is 1
Focus on the first coefficient (1) and the last term (-10)
List out the factors of each: Factors of 1: -1 and 1 Factors of -10: -10, -5, -2, -1, 1, 2, 5, 10
Divide the factors of the last term (-10) over the factors of the first coefficient (1) to get... -10/(-1) = 10 -10/(1) = -10 -5/(-1) = 5 -5/(1) = -5 -2/(-1) = 2 -2/(1) = -2 -1/(-1) = 1 -1/(1) = -1
The unique results we get are: -1, 1, -2, 2, -5, 5, -10, 10
So those are the possible rational roots of x^3+6x^2-x-10 = 0 This rules out choice 2, choice 3, choice 4. The only thing left is choice 1. The value 4 is not a possible rational root of x^3+6x^2-x-10 = 0
