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Math Help - How do you factor x^4-16?

  1. #1
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    How do you factor x^4-16?

    My answer sheet says =(x2)2-(22)2
    = (x2-22)(x2+22)
    =(x-2)(x+2)(x2+2)
    My question is, how did it break that down like that?
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  2. #2
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    Re: How do you factor x^4-16?

    Quote Originally Posted by EJdive43 View Post
    My answer sheet says =(x2)2-(22)2
    = (x2-22)(x2+22)
    =(x-2)(x+2)(x2+2)
    My question is, how did it break that down like that?
    x^4-16=(x^2+4)(x+2)(x-2)
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  3. #3
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    Re: How do you factor x^4-16?

    Difference of squares

    a^2 - b^2 = (a-b)(a+b)
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  4. #4
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    Re: How do you factor x^4-16?

    x^4 - 16

    This is the difference of two squares, which factors to
    (x^2 + 4)(x^2 - 4)

    You can't factor x^2 + 4 anymore, but x^2 - 4 is another difference of squares, which can be factored to (x + 2)(x - 2), the final answer is

    (x^2 + 4)(x + 2)(x - 2)
    Last edited by louisejane; August 9th 2012 at 12:28 AM.
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