Answer: choice 1) 4
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Step-by-step explanation:
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
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
So that's why choice 1 is the answer