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Math Help - Factor theorem to find variable

  1. #1
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    Factor theorem to find variable

    I'm realy stuck to the attached question I know how to do synthetic and long division, and that the remainder is just the value of the function after plugging in x.

    help would be greatly appreciated. thanks.
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  2. #2
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    Re: Factor theorem to find variable

    The remainder of \frac{f(x)}{x+2} is f(-2), or  4 - 2k

    The remainder of \frac{f(x)}{x-2} is f(2), or 20 + 2k

    4-2k is twice that of 20+k, so 4-2k = 2(20+2k) \Rightarrow k = -6.
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