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Thread: Common Factor

  1. #1
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    Common Factor

    Hi
    For the following equations
    $\displaystyle Y=x+x^2-x^4 $
    do the following steps are correct ?
    $\displaystyle x+(x-x^2)(x+x^2)$
    $\displaystyle x+x(1-x)(1+x)$
    $\displaystyle x[1+1-x^2] $
    $\displaystyle x[2-x^2]$

    Thank you
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  2. #2
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    Quote Originally Posted by metallica007 View Post
    Hi
    For the following equations
    $\displaystyle Y=x+x^2-x^4 $
    do the following steps are correct ?
    $\displaystyle x+(x-x^2)(x+x^2)$
    $\displaystyle x+x(1-x)(1+x)$
    $\displaystyle x[1+1-x^2] $
    $\displaystyle x[2-x^2]$

    Thank you
    that's not correct.
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  3. #3
    Super Member Bacterius's Avatar
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    No. The common factor is just $\displaystyle x$.

    $\displaystyle Y=x+x^2-x^4$

    $\displaystyle Y = x(1 + x - x^3)$

    --------------

    When you are unsure about a result, just try with some numbers. With your result, what you are saying is that :

    $\displaystyle x + x^2 - x^4 = x(2 - x^2)$

    Take $\displaystyle x = 2$. Thus we get :

    $\displaystyle 2 + 2^2 - 2^4 = 2(2 - 2^2)$

    And therefore your results suggests that $\displaystyle -10 = -4$

    But $\displaystyle -10 \neq -4$, thus your result is wrong.
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  4. #4
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    Quote Originally Posted by metallica007 View Post
    Hi
    For the following equations
    $\displaystyle Y=x+x^2-x^4 $
    do the following steps are correct ?
    $\displaystyle x+(x-x^2)(x+x^2)$
    $\displaystyle x+x(1-x)(1+x)$ <.... here's your problem
    (what follows is wrong)
    $\displaystyle x[1+1-x^2] $
    $\displaystyle x[2-x^2]$

    Thank you
    $\displaystyle x+(x-x^2)(x+x^2)=x+x^2(1-x)(1+x)=x(1+x(1-x)(1+x))$
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  5. #5
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    Quote Originally Posted by Raoh View Post
    $\displaystyle x+(x-x^2)(x+x^2)=x+x^2(1-x)(1+x)=x(1+x(1-x)(1+x))$
    Thank you for show me the problem
    I was not sure about that step
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