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Math Help - factor this completely

  1. #1
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    Thumbs up factor this completely

    x^3-x^2+2
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  2. #2
    Like a stone-audioslave ADARSH's Avatar
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    Quote Originally Posted by princess_21 View Post
    x^3-x^2+2
    = x^3 + 1 - x^2+1
    =(x+1)(x^2+1-x) - (x+1)(x-1)
    =(x+1) (x^2+1-x-x+1)
    =(x+1)(x^2-2x+2)...
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  3. #3
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    Quote Originally Posted by ADARSH View Post

    = x^3 + 1 - x^2+1
    =(x+1)(x^2+1-x) - (x+1)(x-1)
    =(x+1) (x^2+1-x-x+1)
    =(x+1)(x^2-2x+2)...
    i didn't get the 2nd and 3rd step..
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by princess_21 View Post
    i didn't get the 2nd and 3rd step..
    he factored by grouping.


    x^3 + 1 <--------sum of two cubes. goes to (x + 1)(x^2 - x + 1)

    1 - x^2 <--------difference of two squares. goes to (1 - x)(1 + x)

    in the third step, he factored out the common factor, that is, (x + 1)
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  5. #5
    Like a stone-audioslave ADARSH's Avatar
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    Quote Originally Posted by ADARSH View Post

    = x^3 + 1 - x^2+1
    =(x+1)(x^2+1-x) - (x+1)(x-1)
    =(x+1) (x^2+1-x-x+1)
    =(x+1)(x^2-2x+2)...

    Expansion of
    a^3 + b^3 = (a+b)(a^2+b^2-ab)
    => x^3 +1 = (x+1)(x^2+1-x) ------1
    And that of
    a^2-b^2 = (a+b)(a-b)
    => x^2-1 = (x+1)(x-1)--------------2

    so
    x^3 + 1 - x^2+1
    =(x^3 +1 ) - (x^2-1)
    put 1 and 2 in the equation and then take (x+1) as common
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  6. #6
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    Question

    Quote Originally Posted by Jhevon View Post
    he factored by grouping.


    x^3 + 1 <--------sum of two cubes. goes to (x + 1)(x^2 - x + 1)

    1 - x^2 <--------difference of two squares. goes to (1 - x)(1 + x)

    in the third step, he factored out the common factor, that is, (x + 1)
    how did he factored? why? the third step.
    ??
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  7. #7
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    Thumbs up factor this completely

    thanks.
    Last edited by mr fantastic; January 13th 2009 at 11:24 PM.
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  8. #8
    Like a stone-audioslave ADARSH's Avatar
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    I hope this would help
    x^3-x^2+2 can be written as
    = x^3 +x^2 - 2 x^2 -2x +2x+2
    =x^2(x+1)-2x(x+1)+2(x+1)
    =(x^2-2x+2)(x+1)...
    ...I think you got it before this reply
    Last edited by ADARSH; January 13th 2009 at 10:51 PM. Reason: ...
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