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Math Help - Polynomials

  1. #1
    Junior Member wpcp15's Avatar
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    Question Polynomials

    Im supposed to factor polynomials but I have three problems I cant figure out
    ( when I have ^, it means its an exponent

    Thanks for any help I can get

    #1 12m^2 - m - 6
    Im not sure what to do with the 12


    #2 x^4 - 81


    Im supposed to simplify
    #3 x^2 over (x^2 - x)(x-1)^-1

    Thanks Again
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  2. #2
    Super Member
    earboth's Avatar
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    Quote Originally Posted by wpcp15 View Post
    Im supposed to factor polynomials but I have three problems I cant figure out
    ( when I have ^, it means its an exponent
    Thanks for any help I can get

    #1 12m^2 - m - 6
    Im not sure what to do with the 12
    #2 x^4 - 81
    Im supposed to simplify
    #3 x^2 over (x^2 - x)(x-1)^-1
    Thanks Again
    Hello, wpcp,

    to 1.: You can put the 12 before paranthese and afterwards factor the contents of the bracket as usual:
    12m^2 - m - 6=12 \cdot \left(m^2-\frac{1}{12}m-\frac{1}{2}\right) =12 \left(m+\frac{2}{3}\right) \left(m-\frac{3}{4}\right)

    to 2.: Remember that x^4 = (x^2)^2 and of course 81 = 9^2. So you've got a binomial formula:
    x^4-81=\left(x^2\right)^2-9^2=(x^2+9)(x^2-9)

    to 3.: Rewrite this term:

    \frac{x^2}{(x^2 - x)(x-1)^{-1}}=\frac{x^2}{(x^2 - x)\cdot \frac{1}{x-1}} = \frac{x^2 \cdot (x-1)}{x(x-1)} = x,\ \ x\neq 0\ \wedge \ x\neq1

    EB
    Last edited by earboth; November 8th 2006 at 11:24 AM.
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