SOLUTION: Determine whether the statement is true or false. If x - 3 is a factor of a polynomial f(x), then f(-3) = 0.

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Question 1079554: Determine whether the statement is true or false.
If x - 3 is a factor of a polynomial f(x), then f(-3) = 0.
Answer by ikleyn(52788)   (Show Source): You can put this solution on YOUR website!
.
1.  This statement, as it presented in the post, might be TRUE and MIGHT be FALSE,

    DEPENDING on the polynomial f(x).


    For example,  if f(x) = , then (x-3) is the factor of f(x), but f(-3) =  =  = 36 is not zero.


    From the other side, if f(x) = (x-3)*(x+3), then (x-3) is the factor of f(x), and f(-3) = (3-(-3))*(3+(-3)) = 0.




2.  But, if I modify the statement in this way:


         Determine whether the statement is true or false.

              If x - 3 is a factor of a polynomial f(x), then f(3) = 0


    then this MODIFIED statement is TRUE.


    It follows from the "Remainder theorem".


On "Remainder theorem" see the lesson
    - Divisibility of polynomial f(x) by binomial (x-a). The Remainder theorem
in this site.


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