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Math Help - help Factoring this equation

  1. #1
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    help Factoring this equation

    how do i factor this using synthetic division?
    4x^4-16x^3+7x^2+4x-2 = 0


    i will divide it by 2x - 1 but why?

    after dividing it by 2x-1 i got a result of

    2x^3 - 7x^2 + 2

    i divide it by 2x+1 but why?


    and i know this is trial and error
    please help
    Last edited by ^_^Engineer_Adam^_^; February 3rd 2008 at 01:57 AM.
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  2. #2
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    Quote Originally Posted by ^_^Engineer_Adam^_^ View Post
    how do i factor this using synthetic division?
    4x^4-16x^3+7x^2+4x-2 = 0


    i will divide it by 2x - 1 but why?

    after dividing it by 2x-1 i got a result of

    2x^3 - 7x^2 + 2

    i divide it by 2m+1 but why?


    and i know this is trial and error
    please help
    Note that 4x^4-16x^3+7x^2+4x-2 = (4x^4-16x^3+8x^2) - x^2 +4x-2

    = 4x^2 (x^2 - 4x + 2) - (x^2 - 4x + 2)

     = (4x^2 - 1)(x^2 - 4x + 2)

    = (2x - 1)(2x + 1)([x^2 - 4x + 4] - 2)

    = (2x - 1)(2x + 1)([x - 2]^2 - 2)

     = (2x - 1)(2x + 1)(x - 2 - \sqrt{2})(x - 2 + \sqrt{2}).
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