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Math Help - factoring

  1. #1
    Newbie 21_knip's Avatar
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    factoring

    can someone tell me how to factor this?
    (x-3)(x-1)(x+1)(x+3)+64
    thanks.
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  2. #2
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    Quote Originally Posted by 21_knip View Post
    can someone tell me how to factor this?
    (x-3)(x-1)(x+1)(x+3)+64
    thanks.
    If you expand and simplify (and there's an easy way to do this by hand) you get x^4 - 10x^2 + 73.

    This can be factorised as two irreducible real quadratics factors and four complex linear factors otherwise.
    Last edited by mr fantastic; January 13th 2009 at 09:29 PM. Reason: Fixed typo
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  3. #3
    Newbie 21_knip's Avatar
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    is this the final answer when it is said to factor completely? ur answer, is it still factorable?
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  4. #4
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    Quote Originally Posted by 21_knip View Post
    is this the final answer when it is said to factor completely? ur answer, is it still factorable?
    Is the quartic I have given yu to be factorised over real or complex numbers? Start by thinking how to factorise into two irreducible quadratics.
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  5. #5
    Newbie 21_knip's Avatar
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    factoring

    if i changed 64 to 16 what would be the answer?
    (x-3)(x-1)(x+1)(x+3)+16

    my answer is (x^2-3)(x^2-5)
    is this correct?
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  6. #6
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    Quote Originally Posted by 21_knip View Post
    if i changed 64 to 16 what would be the answer?
    (x-3)(x-1)(x+1)(x+3)+16

    my answer is (x^2-3)(x^2-5)
    is this correct?
    No. The quartic becomes x^4 - 10x^2 + 25 and this has a very simple factorisation (think perfect square) ....
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