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Math Help - Pre-Calc Help Please!

  1. #1
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    Pre-Calc Help Please!

    I had a problem that states: "Determine all values of k such that x^2-kx-6 can be factored by x-2." I had no idea what the answer was and left it blank. Can you please tell me how i would go through doing a problem like that. Thank you.
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  2. #2
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    Quote Originally Posted by aussiekid90
    I had a problem that states: "Determine all values of k such that x^2-kx-6 can be factored by x-2." I had no idea what the answer was and left it blank. Can you please tell me how i would go through doing a problem like that. Thank you.
    Remember by the theory of polynomial (x-2) is a factor of f(x)=x^2-kx-6 only if 2 is a zero of this polynomial, thus, f(2)=0, thus, 4-2k-6=0 thus, k=-1.

    Now for the check, the polynomial is x^2+x-6 which factors into (x+3)(x-2) thus, it works.
    Q.E.D.
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  3. #3
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    Would this be the only possiblity because the problem states find all possible solutions for K
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  4. #4
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    Quote Originally Posted by aussiekid90
    Would this be the only possiblity because the problem states find all possible solutions for K
    Yes, look at my derivation, only one possibility.
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