SOLUTION: Question 1089091: If the f(x)=x^5 +bx^4 +cx^3 +dx^2 +ez+k, f(-1)=0, and f(3)=0, then f(x) is divisible by? A)x-2 B)x+3 C)x^2 + 3x+2 D)x^2 -2x-3

Question 1089167: Question 1089091: If the f(x)=x^5 +bx^4 +cx^3 +dx^2 +ez+k, f(-1)=0, and f(3)=0, then f(x) is divisible by?
A)x-2
B)x+3
C)x^2 + 3x+2
D)x^2 -2x-3
Answer by ikleyn(52898) (Show Source): You can put this solution on YOUR website!
.

1.  Since f(-1) = 0, then f(x) is divisible by (x+1)    (the "Remainder theorem")


2.  Since f(3) = 0, then f(x) is divisible by (x-3).    ( due to the same reason )


3.  Therefore, f(x) is divisible by the product (x+1)*(x-3) = x^2 - 2x - 3.


4.  Option D) of your list.


5.  And no other options.

----------------

    My previous answer/response to this problem at the link
  
https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1089091.html

    was wrong and incorrect.


    Sorry for that.


    I deleted that response.

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