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Math Help - a+1 is not a factor of a^2+1

  1. #1
    MHF Contributor alexmahone's Avatar
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    a+1 is not a factor of a^2+1

    a+1 is not a factor of a^2+1.

    However, when a=-3, we get -2 is not a factor of 10, which is false. Could someone explain this anomaly?
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  2. #2
    MHF Contributor

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    Re: a+1 is not a factor of a^2+1

    the polynomial in a, a+1, is not a factor of the polynomial in a, a^2 + 1.

    this does not mean that for some particular NUMBER a, a+1 is not a factor of a^2 + 1, which is clearly false: for example a = 1 gives 2 divides 2, which is true.

    there is a difference between the function defined by f(a) = a+1, and the value f(a) for some particular a.

    two unequal functions can nevertheless have intersecting graphs.
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  3. #3
    MHF Contributor Siron's Avatar
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    Re: a+1 is not a factor of a^2+1

    Because it's not true for all the values you'll give to a, take for example a=5 then a+1=6 which is not a factor of a^2+1=26. If you take for example a^2-1, then a-1 is a factor, so for every value of a it will still be a factor.
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