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Math Help - having problems factoring these 2 equations

  1. #1
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    having problems factoring these 2 equations

    y= x^3 - x^2
    y=(x-2)^3 - (x-2)^2

    these are 2 functions for which i am trying to find the roots
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  2. #2
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by tappinniamke View Post
    y= x^3 - x^2
    y=(x-2)^3 - (x-2)^2

    these are 2 functions for which i am trying to find the roots
    y = {x^3} - {x^2} = (x^2)(x-1)

    y = (x-2)^{3} - {(x-2)^{2}}= {(x-2)^{2}}((x-2)-1)= (x-2)(x-2)(x-3)
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  3. #3
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    thanks i made it alot more complicated in my head than it needed to be
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  4. #4
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    just with the second question...
    (x-2)^3 - (x-2)^2

    sometimes it helps to give the common factor, in this case (x-2) a letter say for example z. this just makes factorizing a little easier.

    for example:

    let (x-2) = z
    so the new equation (if we sub in z whenever we see a (x-2) becomes:
    z^3 - z^2
    so this factorized becomes
    z^2(z-1)
    and now sub in for z (x-2)
    (x-2)^2((x-2)-1)
    which is equal to:
    (x-2)^2(x-3)

    hope that helps a little for in the future!
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