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Math Help - Finding the values of p and q.

  1. #1
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    Finding the values of p and q.

    The expressions px^4-5x+q and x^4-2x^3-px^2-8 have a common factor x-2. Find the values of p and q.
    What would be the best way to answer this question? Do I use simultaneous equations?
    I'm just really stuck on this one.
    Thanks in advance everyone.
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  2. #2
    Super Member Quacky's Avatar
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    Windsor, South-East England
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    Use the Factor Theorem

    Let f(x)=px^4-5x+q and g(x)=x^4-2x^3-px^2-8

    By using the information in the question and the factor theorem, f(2) and g(2)=0

    1) f(2)=p(2)^4-5(2)+q=0
    2) g(2)=(2)^4-2(2)^3-p(2)^2-8=0

    Two equations, two unknowns: simplify then solve for p and q.
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  3. #3
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    Thank you so much.
    That's how I was thinking it had to be done, but I just couldn't work it out.
    You are brilliant.
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