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Math Help - Factoring using 0

  1. #1
    Member agentmulder's Avatar
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    Factoring using 0

    Here is a trick to factor x^3 + 1

    subtract x and add x

    1) x^3 - x + x + 1

    group

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

    factor

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

    4) x(x - 1)(x + 1) + (x + 1)

    5) (x + 1)[x(x -1) + 1]

    6) (x + 1) (x^2 - x + 1)


    The same clever use of 0 can help you factor x^3 - 1

    Clever use of 0 can help you factor x^4 + x^2 + 1 by subtracting and adding x

    1) x^4 + x + x^2 - x + 1

    group

    2) (x^4 + x) + (x^2 - x + 1)

    factor

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

    4) x(x +1)(x^2 - x + 1) + (x^2 - x + 1)

    5) (x^2 - x + 1)(x^2 + x + 1)

    Many other factorizations are possible using 0
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  2. #2
    MHF Contributor
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    Re: Factoring using 0

    Try multiplication using Unity! Both very useful techniques.
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  3. #3
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    Re: Factoring using 0

    Is the OP asking a question?
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  4. #4
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    Re: Factoring using 0

    Quote Originally Posted by agentmulder View Post
    Here is a trick to factor x^3 + 1

    subtract x and add x

    1) x^3 - x + x + 1

    group

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

    factor

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

    4) x(x - 1)(x + 1) + (x + 1)

    5) (x + 1)[x(x -1) + 1]

    6) (x + 1) (x^2 - x + 1)


    The same clever use of 0 can help you factor x^3 - 1

    Clever use of 0 can help you factor x^4 + x^2 + 1 by subtracting and adding x

    1) x^4 + x + x^2 - x + 1

    group

    2) (x^4 + x) + (x^2 - x + 1)

    factor

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

    4) x(x +1)(x^2 - x + 1) + (x^2 - x + 1)

    5) (x^2 - x + 1)(x^2 + x + 1)

    Many other factorizations are possible using 0
    Hiii Agentredlum ! Good to see you here !
    x^3+1 is an identity a^3+b^3
    So
    it will be
    (x+1)(x^2+1-x)
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  5. #5
    Member agentmulder's Avatar
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    Re: Factoring using 0

    Hello there sankalpmittal, I guess my point is that it is possible to use 'nothing' to get 'something'

    I LOVE your circle area derivation, I am very impressed.:smile:
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  6. #6
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    Re: Factoring using 0

    Quote Originally Posted by agentmulder View Post
    Hello there sankalpmittal, I guess my point is that it is possible to use 'nothing' to get 'something'

    I LOVE your circle area derivation, I am very impressed.:smile:
    May I know why were you banned from physics forums ? Just because your quadratic formula was different from textbook definition ?!

    We will also prove that whether your formula is right . Just ask Dr. Math , he is a genius in mathematics. Ask him here : The Math Forum: Write to Dr. Math

    If he agrees that your formula is well simplified from textbook definition , then rest of the forum members must confess.

    Dr. Math will reply in your id within 1 day.

    Cheers !
    Last edited by sankalpmittal; September 25th 2011 at 11:17 PM.
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