SOLUTION: given f(x) is a factor of P(x); suppose that f(2) =0. does that imply that P(2)=0? why or why not?

Question 816803: given f(x) is a factor of P(x); suppose that f(2) =0. does that imply that P(2)=0? why or why not?
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
Since factors come in pairs, if f(x) is a factor of P(x) then there must be another factor. Let's call this other factor g(x). Then
P(x) = f(x)*g(x)
This means
P(2) = f(2)*g(2)
And since we know that f(2) = 0:
P(2) = 0*g(2)
From this we can see that it makes no difference what g(2) is. If you multiply it by 0 you get zero:
P(2) = 0
So yes, if a factor of P(2) is zero, then P(2) must be zero.

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