Question 1079554
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<pre>
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) = {{{(x-3)^2}}}, then (x-3) is the factor of f(x), but f(-3) = {{{(-3-3)^2}}} = {{{6^2}}} = 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 <U>modify</U> 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 <U>MODIFIED</U> statement is TRUE.


    It follows from the "Remainder theorem".
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On "Remainder theorem" see the lesson 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Divisibility-of-polynomial-f%28x%29-by-binomial-x-a.lesson>Divisibility of polynomial f(x) by binomial (x-a). The Remainder theorem</A>

in this site.