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Math Help - Factorize

  1. #1
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    Factorize

    How does:

    x^3 - 9x^2 + 24x -16

    Become:

    (x - 1) (x^2 - 8x - 16)

    And what are the values of x?

    What would be good study material for this type of algebra?
    Last edited by anon_404; May 13th 2009 at 05:36 AM.
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  2. #2
    Member TheMasterMind's Avatar
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    Quote Originally Posted by anon_404 View Post
    How does:

    x^3 - 9x^2 + 24x -16

    Become:

    (x - 1) (x^2 - 8x - 16)

    And what are the values of x?

    What would be good study material for this type of algebra?
    The most efficent way to do this I would presume would be to use the method of synthetic division for dividing polynomials. Have you learned this method?
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  3. #3
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    Quote Originally Posted by TheMasterMind View Post
    The most efficent way to do this I would presume would be to use the method of synthetic division for dividing polynomials. Have you learned this method?
    I havn't used that method.
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  4. #4
    Super Member craig's Avatar
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    Synthetic Division

    There is a good example on synthetic division found here.
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  5. #5
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by anon_404 View Post
    How does:

    x^3 - 9x^2 + 24x -16

    Become:

    (x - 1) (x^2 - 8x - 16)

    And what are the values of x?

    What would be good study material for this type of algebra?
    Are you sure that's a correct factorisation? Look at the last terms: -1 x -16 = +16 not -16 as stated in the question
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  6. #6
    MHF Contributor

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    Quote Originally Posted by anon_404 View Post
    How does:

    x^3 - 9x^2 + 24x -16

    Become:

    (x - 1) (x^2 - 8x - 16)
    It doesn't! It is easy to see quickly that the constant term in that product is (-1)(-16)= +16, not -16 as in the first expression. It is true that
    x^3- 9x^2+ 24x+ 16= (x-1)(x^2- 8x- 16)
    The best way to see this is to multiply it back:
    (x-1)(x^2- 8x- 16)= (x)(x^2- 8x- 16)- (x^2- 8x- 16)
    = x^3- 8x^2- 16x- x^2+ 8x+ 16= x^2- (8+1)x^2- (16-8)x+ 16
    [tex]= x^3- 9x^2- 8x+ 16[/itex]

    And what are the values of x?
    ??? x can be any number! Did you mean "what are the values of x that make this 0" or "what values of x solve x^3- 9x^2- 8x+ 16= 0?

    In this case you can also factor x^2- 8x- 16= (x- 4)^2 so
    x^3- 8x- 16= (x- 1)(x^2- 8x- 16)= (x-1)(x-4)^2= 0 and you can use the fact that "if ab= 0 then either a= 0 or b= 0".

    What would be good study material for this type of algebra?[/QUOTE]
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