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Math Help - Factorising

  1. #1
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    Factorising

    Express x^4 - x in its fully factorise form.

    I went through factorising methods:

    common factor
    difference of two squares X
    breaking brackets X
    quadratic formula X
    polynomial ?

    I would say answer = x(x^3 - 1)
    But that is way to simple for the level i'm taking, so im asking if polynomials are involved here? If not, what else should i try?
    Please don't show me the solution, just answer yes/no.
    Thanks
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  2. #2
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    Quote Originally Posted by r_maths View Post
    Express x^4 - x in its fully factorise form.

    I went through factorising methods:

    common factor
    difference of two squares X
    breaking brackets X
    quadratic formula X
    polynomial ?

    I would say answer = x(x^3 - 1)
    But that is way to simple for the level i'm taking, so im asking if polynomials are involved here? If not, what else should i try?
    Please don't show me the solution, just answer yes/no.
    Thanks
    You can do more.
    a^3-b^3=(a-b)(a^2+ab+b^2)
    Thus,
    x(x^3-1)=x(x-1)(x^2+x+1)
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  3. #3
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    Quote Originally Posted by ThePerfectHacker View Post
    You can do more.
    x(x^3-1)=x(x-1)(x^2+x+1)

    (x^2+x+1)
    that could also factorise more?

    (x+1) (x+1)
    ?
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  4. #4
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    Quote Originally Posted by r_maths View Post
    (x^2+x+1)
    that could also factorise more?

    (x+1) (x+1)
    ?
    No. (x+1)(x+1)=(x+1)^2=x^2 +2x + 1 =/= x^2 + x +1
    if you like to play with that you can always write
    ((x+1)^2) - x
    but I would leave it the way it is x^2 + x +1
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  5. #5
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    Quote Originally Posted by Aglaia View Post
    No. (x+1)(x+1)=(x+1)^2=x^2 +2x + 1 =/= x^2 + x +1
    if you like to play with that you can always write
    ((x+1)^2) - x
    but I would leave it the way it is x^2 + x +1
    cheers, i should of checkd with FOIL
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