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Math Help - find r .... exponents

  1. #1
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    find r .... exponents

    find r .... exponents-screen-shot-2010-09-12-12.57.33-pm.png


    I can't figure out the right approach...

    put in a screen shot because I'm not sure about notation on the forum

    Thanks!
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  2. #2
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    e^(i*pi)'s Avatar
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    This is a long division problem (you'll also find a,b and c as a bonus). In this case r will be your final remainder

    Since it's a nightmare to do on latex I'll link to Wolfram: http://www.wolframalpha.com/input/?i...29%2F%28x-4%29
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  3. #3
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    \displaystyle \frac{3x^3-2x^2+2x-2}{x-4} = ax^2+bx+c+\frac{r}{x-4}

    \displaystyle \Rightarrow 3x^3-2x^2+2x-2 = (x-4)(ax^2+bx+c)+r

    \displaystyle \Rightarrow 3x^3-2x^2+2x-2 = ax^3+(b-4a)x^2+(c-4b)x-4c+r

    Comparing the coefficients:

    It's obvious that a = 3.

    Therefore b-4a = -2 \Rightarrow b = 10.

    So c-4b = 2 \Rightarrow c = 42.

    Finally -4c+r = -2 \Rightarrow r = 166.
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