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Factoring a third degree polynomial as part of a limits problem

  1. Dec 16, 2011 #1
    1. The problem statement, all variables and given/known data

    I have a limit problem, however I do know how to work limits, I guess what I need is more of a refresher on how to work third degree polynomials. The polynomial(s) I am trying to work with are the following:

    x3-2x2+2x-15
    -and-
    x3-5x2+10x-12

    The limit is a limit where x approaches 3, so I believe that it is correct to assume that 3 is the rational root that we use in this case. However, my attempts haven't come up with a correct solution. I am just wondering where I have gone wrong and what I need to do to reach the correct answer.

    2. The attempt at a solution

    x3-2x2+2x-15
    x3-2x2+2x-15 ÷ x+3

    First, I divide to get x2, then multiply x-3 by this to reach x3-3x2
    Then I bring down 2x to get x2+2s
    Next I divide again to get x, then multiply x-3 again to reach x2-3x
    Finally I bring down -15 to get x-15. However if I divide again I get 1, but 1•-3 does not equal -15 so I get a remainder of 12.

    What am I doing wrong here?
     
  2. jcsd
  3. Dec 16, 2011 #2

    LCKurtz

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    A root x = 3 corresponds to a factor of (x-3). Try that.
     
    Last edited: Dec 16, 2011
  4. Dec 16, 2011 #3

    vela

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    When you subtracted [itex]x^2-3x[/itex] from [itex]x^2+2x[/itex], you made a sign error.
     
  5. Dec 16, 2011 #4

    dextercioby

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    If you can't get a hold on what <polynomial long division> means, then try this thing

    [tex] x^3 - 2x^2 + 2x -15 = (x-3) (Ax^2 + Bx + C) [/tex]

    No matter what value of x. Then try x=0, x=1, x=-1...
     
  6. Dec 16, 2011 #5
    edit - never mind
     
  7. Dec 17, 2011 #6
    Thanks to all of you. I realize now what my errors were.
     
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