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Help: (x-3) is a factor of x^2-4x+c, find c?

  1. Sep 14, 2012 #1
    1. The problem statement, all variables and given/known data

    If (x-3) is a factor of: x^2 - 4x + c, what is c?





    2. Relevant equations



    3. The attempt at a solution

    I am really stuck here. When presented with these types of questions, what is the FIRST thing you look at/do ?

    Thanks so much.
     
  2. jcsd
  3. Sep 14, 2012 #2

    Mark44

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    There's a theorem that deals with this. If x - a is a factor of a polynomial f(x), then f(a) = 0.

    Here's an example:
    f(x) = x3 - x2 - 5x - 3

    As it happens, f(x) can be factored into (x - 3)(x2 + 2x + 1).

    This means that x - 3 is a factor of f(x). It also means that f(3) = 0. We can verify this by calculating f(3) = 33 - 32 - 5(3) - 3 = 27 - 9 - 15 - 3 = 0.
     
  4. Sep 14, 2012 #3

    SammyS

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    The first thing I ask, is what do you know about polynomials and factoring.

    For this problem, "What is the remainder of (x2 - 4x + c)÷(x-3), if (x-3) is a factor of x2 - 4x + c ?"
     
  5. Sep 14, 2012 #4
    Holy crap, think I got it. Please let me know if correct?

    If (x-3) is a factor of: x^2 - 4x + c, what is c?


    (3)^2 - 4(3) + c

    9 - 16 + c = 0

    c = 7

    ? is that correct????
     
  6. Sep 14, 2012 #5

    LCKurtz

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    Do you really have to ask that? Is x-3 a factor of ##x^2-4x+7##? If it is you are done, otherwise you might want to check your arithmetic.
     
  7. Sep 14, 2012 #6

    SammyS

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    What is 4(3) ?

    (It's not 16.)
     
  8. Sep 14, 2012 #7
    Oh, I wrote on my paper 4(4)
     
  9. Sep 14, 2012 #8
    So correct answer is:

    c = +3

    Umm... sorry if this is a dumb question, but the last 2 I did, C is always the same as what they are telling is a factor of.

    So, this one I just did, they say (x+3) is a factor of..... would c automatically be +3?

    The answer turned out to be +3.

    Can someone give me another simular example to try???
     
  10. Sep 14, 2012 #9

    SammyS

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    Work some examples out for yourself.

    What is (x-3)(x+4) ?

    The one you were solving in this thread has a factor of (x-3).

    But, suppose the question is:
    If (x+3) is a factor of: x2 - 4x + c, what is c?

    If f(x) = x2 - 4x + c, what is f(-3) ?​
     
  11. Sep 15, 2012 #10
    Hi sammy.

    Ok, so for the question you gave me: If (x+3) is a factor of: x2 - 4x + c, what is c?

    c would = -21 ?
     
  12. Sep 15, 2012 #11

    SammyS

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    Yes.
     
  13. Sep 15, 2012 #12

    LCKurtz

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    Nukeman, I will suggest again, when you have a problem like that and you think c = -21 so your function is ##x^2-4x-21##, why don't you just try factoring it yourself and see if x+3 is a factor instead of asking us if -21 is correct?
     
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