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Polynomial Factors

  1. Oct 11, 2007 #1
    This problem came up on a math contest the other day and I drew a blank - now it's bugging me.

    "If the polynomial P(x)=x^2+ax+1 is a factor of T(x)=2x^3-16x+b, find the values of a and b."

    Anyone have any ideas?
     
  2. jcsd
  3. Oct 11, 2007 #2
    We have that there is a c such that (x^2+ax+1)(2x+c)=2x^3-16x+b. Thus comparing coefficients gives us:

    c+2a=0
    2+ac=-16
    b=c

    Solving this yields

    a=3 or -3, and thus
    b=-6 or 6
     
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