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Easy Factorization Question

  1. Feb 27, 2008 #1
    Factorize:



    x^3 − 2x^2 − 4x + 8


    correct answer:

    (x^3 − 2x^2) − (4x − 8)

    x^2(x − 2) − 4(x − 2)

    (x^2 − 4)(x − 2)

    (x − 2)(x + 2)(x − 2)

    (x − 2) 2(x + 2)

    In the third line where the terms are grouped i dont understand why one of the (x - 2) is omitted? i.e shouldn't it be (x -2)^2 ?
     
    Last edited: Feb 27, 2008
  2. jcsd
  3. Feb 27, 2008 #2
    Sorry just realized this should be under the "homework" section. Will post homework questions there in future (in the meantime could a mod please move it there)..
     
    Last edited: Feb 27, 2008
  4. Feb 27, 2008 #3
    can anyone help please? Its too critical and basic to go any further in the course notes until i understand this
     
  5. Feb 27, 2008 #4
    .... What is ^????
     
  6. Feb 27, 2008 #5

    CRGreathouse

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    (x^2 - 4) = (x - 2)(x + 2), so one of the (x - 2) factors was "hiding inside" the (x^2 - 4).
     
  7. Feb 27, 2008 #6
    Going from:x^2(x − 2) − 4(x − 2)
    to:(x^2 − 4)(x − 2)
    is your problem? Well consider this:
    ab - cb = b(a - c)
    Do you agree? If we multiply out on the right we get the left-hand side. Now in your example, a = x^2, b=(x-2), c=4.
    Do you see how it works now?
     
  8. Feb 27, 2008 #7


    thank you
     
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