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Simplifying a ?quad?nomial

  1. Apr 18, 2012 #1
    1. The problem statement, all variables and given/known data

    simplify -x^3 - 3x^2 - 4x - 2
    It is equal to -(x-1)(x^2 + 2x + 2)

    Not sure how to get that answer, nor how to start it.
     
  2. jcsd
  3. Apr 19, 2012 #2

    Mentallic

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    The word you're looking for is to factorize it, not simplify it. You can't simplify it in the sense that you can simply [tex]\frac{\sin(x)}{\cos(x)}[/tex] to become [tex]\tan(x)[/tex] for example.

    Ok so first of all, in order to factorize that cubic you'll need to know one of its roots. Do you know how to check if a polynomial has rational roots?
     
  4. Apr 19, 2012 #3

    HallsofIvy

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    Good! Because you shouldn't get that "answer". It is wrong.

    Setting x= 1 in that polynomial gives -(1)- 3(1)- 4(1)- 2= -(1+3+ 4+ 2)= -10, not 0. Since x= 1 does NOT make that polynomial 0, x- 1 is NOT a factor. -x^3- 3x^2- 4x- 2 is NOT equal to -(x- 1)(x^2+ 2x+ 2).

    However, setting x= -1 gives -(-1)- 3(1)- 4(-1)- 2= 1- 3+ 4- 2= 0 so x-(-1)= x+ 1 is a factor. Divide -x^3- 3x^2- 4x- 2 by x+1 to get the other factor.
     
  5. Apr 19, 2012 #4

    Mentallic

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    Ah yes I shouldn't noticed that at quick glance since [tex]-x^3 - 3x^2 - 4x - 2 = -(x^3+3x^2+4x+2)[/tex] which should have all same sign coefficients in its factors
     
  6. Apr 19, 2012 #5

    SammyS

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    -(x-1)(x^2 + 2x + 2)

    is equivalent to:

    -x^3 -x^2 + 2
     
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