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Math Help - Factoring Problem

  1. #1
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    Factoring Problem

    How does

    1 - 9x^{2} + 24x^{4} - 16x^{6}

    become

    (1 - x^{2})(16x^{4} - 8x^{2} + 1) ?
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  2. #2
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    Re: Factoring Problem

    Quote Originally Posted by Jason76 View Post
    How does
    1 - 9x^{2} + 24x^{4} - 16x^{6}
    become
    (1 - x^{2})(16x^{4} - 8x^{2} + 1) ?
    @Jason76, you are basically lazy are you not?

    You demand to know "How does...become"?

    Are you to lazy to multiply (1 - x^{2})(16x^{4} - 8x^{2} + 1) out to see how it all works?
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  3. #3
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    Re: Factoring Problem

    Hey Jason76.

    You might want to look at this:

    Rational root theorem - Wikipedia, the free encyclopedia
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  4. #4
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    Re: Factoring Problem

    1 - 9x^{2} + 24x^{4} - 16x^{6}

    Pulling out x^{2}

    1 - [x^{2}(9 + 24x^{2} - 16x^{4})]


    (1 - x^{2})(9 + 24x^{2} - 16x^{4})

    After that, nothing in the right linear has any common factor, so you can't do anymore. But that's not the final answer.
    Last edited by Jason76; November 10th 2012 at 04:49 PM.
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  5. #5
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    Re: Factoring Problem

    Quote Originally Posted by Jason76 View Post
    1 - 9x^{2} + 24x^{4} - 16x^{6}

    Pulling out x^{2}

    1 - [x^{2}(9 + 24x^{2} - 16x^{4})]


    (1 - x^{2})(9 + 24x^{2} - 16x^{4})

    After that, nothing in the right linear has any common factor, so you can't do anymore. But that's not the final answer.
    You did nothing about replay #2.
    Are you really that lazy?
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  6. #6
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    Re: Factoring Problem

    Quote Originally Posted by Plato View Post
    You did nothing about replay #2.
    Are you really that lazy?
    You can't do anymore cause there are no more common factors from what I see. 9, 24, and 16 have no common factor.
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  7. #7
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    Re: Factoring Problem

    Quote Originally Posted by Jason76 View Post
    You can't do anymore cause there are no more common factors from what I see. 9, 24, and 16 have no common factor.
    Here is your basic problem.
    If you do not have a complete understanding of how multiplication works, then you cannot understand factoring.
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  8. #8
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    Re: Factoring Problem

    Quote Originally Posted by Jason76 View Post
    How does

    1 - 9x^{2} + 24x^{4} - 16x^{6}

    become

    (1 - x^{2})(16x^{4} - 8x^{2} + 1) ?
    Hello Jason!
    First you use rational root theorem to find roots then you will use long polynom division to divide the root out.
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