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Math Help - Shortcut for Factoring Polynomials

  1. #1
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    Shortcut for Factoring Polynomials

    Hi,
    Quick question.

    Say we have a polynomial k^2 + k - 12 , one can use FOIL to find the factors.

    However, is there a shortcut for doing the opposite.

    i.e. I have  (k-3)(k+4) but want to find the polynomial? What confused me is that  - 3.-4 will give -12 but so will +3.-4.

    Thanks
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  2. #2
    Bar0n janvdl's Avatar
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    Quote Originally Posted by dumluck View Post
    Hi,
    Quick question.

    Say we have a polynomial k^2 + k - 12 , one can use FOIL to find the factors.

    However, is there a shortcut for doing the opposite.

    i.e. I have  (k-3)(k+4) but want to find the polynomial? What confused me is that  - 3.-4 will give -12 but so will +3.-4.

    Thanks
    A minus times a minus cannot give you a minus. It gives you a plus.

    -3 x -4 = +12
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  3. #3
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    Quote Originally Posted by dumluck View Post
    Say we have a polynomial k^2 + k - 12 , one can use FOIL to find the factors.
    However, is there a shortcut for doing the opposite.
    i.e. I have  (k-3)(k+4) but want to find the polynomial? What confused me is that  - 3.+4 will give -12 but so will +3.-4
    Look at the linear term, \mathbf+k. That + tells us that it is -3,~+4. Do you see why?
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  4. #4
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    Quote Originally Posted by Plato View Post
    Look at the linear term, \mathbf+k. That + tells us that it is -3,~+4. Do you see why?
    Thanks Plato. I don't see why I'm afraid. could +k not equally denote that is could be -4, +3? It would equate to -12?
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  5. #5
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    Quote Originally Posted by dumluck View Post
    Thanks Plato. I don't see why I'm afraid. could +k not equally denote that is could be -4, +3? It would equate to -12?
    If you add +3~\&~-4 we get -1 not +1k. But -3+4=+1k.
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  6. #6
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    Quote Originally Posted by Plato View Post
    If you add +3~\&~-4 we get -1 not +1k. But -3+4=+1k.
    ah ok so  (k + (b))(k + (c)) must translate to  (k)^2 + (b+c)k + (b.c) ?
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