SOLUTION: Use the Factor Theorem to determine whether x-2 is a facor of P(x)=x^3-3x^2-4x+12 Specifically, evaluate P at the proper value, and determine whether x-2 is a factor. This

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Use the Factor Theorem to determine whether x-2 is a facor of P(x)=x^3-3x^2-4x+12 Specifically, evaluate P at the proper value, and determine whether x-2 is a factor. This      Log On


   

Question 400622: Use the Factor Theorem to determine whether x-2 is a facor of
P(x)=x^3-3x^2-4x+12
Specifically, evaluate P at the proper value, and determine whether x-2 is a factor.

This probelm asks me to find P(?)=? as well as figuring out if x-2 is a factor or not.

Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
If (x-2) is a factor of P(x), then what do you think P(x) will be if x = 2? If x is 2 then won't x-2 be zero? And if a factor of of P(x) is zero, won't P(x) be zero, too (regardless of what the other factor is)?

So the "proper value" to test is x=2. If P(2) = 0 then x-2 must be a factor and if P(2) is not zero then x-2 is not a factor.

P%282%29+=+%282%29%5E3-3%282%29%5E2-4%282%29%2B12
I'll leave it up to you so simplify this and find out if x-2 is a factor.

P.S. As I indicated above you use P(2) to see if (x-2) is a factor. P(-2) checks to see if (x-(-2)) or (x+2) is a factor. P(-2) does not check for a factor of (x-2)! Please redo the problem and see what P(2) works out to be!