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Thread: polynomial

  1. #1
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    Post polynomial

    help with another one please, Express as a polynomial.
    (x+a){x^2-ax/x}, my answer is x^2-2ax+a^2, but not sure if it could be x^2-2ax-a^2, thanks for checking.
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by wayne View Post
    help with another one please, Express as a polynomial.
    (x+a){x^2-ax/x}, my answer is x^2-2ax+a^2, but not sure if it could be x^2-2ax-a^2, thanks for checking.
    If you've been doing factoring you should know how to multiply these out. (I mean, without relying on FOIL, but it depends on how you're being taught.)

    $\displaystyle (x + a) \left ( \frac{x^2 - ax}{x} \right )$

    $\displaystyle = \frac{(x + a)(x^2 - ax)}{x}$

    $\displaystyle = \frac{x(x^2 - ax) + a(x^2 - ax)}{x}$

    $\displaystyle = \frac{(x^3 - ax^2) + (ax^2 - a^2x)}{x}$

    $\displaystyle = \frac{x^3 - a^2x}{x}$

    $\displaystyle = \frac{x(x^2 - a^2)}{x}$

    $\displaystyle = x^2 - a^2$

    -Dan

    Edit: Or I suppose you could've simply done
    $\displaystyle \frac{x^2 - ax}{x} = x - a$
    immediately and multiplied out from there.
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  3. #3
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    Smile I should have,

    so I should have x^2-a^2, thanks for looking this over.
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by wayne View Post
    so I should have x^2-a^2, thanks for looking this over.
    No prob!

    -Dan
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