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Homework Help: Polynomial Remainders

  1. Dec 12, 2008 #1

    Mentallic

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    1. The problem statement, all variables and given/known data
    a) Find the remainder when [tex]P(x)=2x^4-7x^3+ax^2+3x-9[/tex] is divided by [tex]2x-1[/tex]

    b) If the remainder, when [tex]P(x)[/tex] is divided by [tex]x+2[/tex], is 17, find the value of a.

    2. Relevant equations
    If a polynomial [tex]P(x)[/tex] is divided by [tex](x-a)[/tex], the resultant is [tex](x-a)Qx+R(x)[/tex]

    3. The attempt at a solution
    For a) I substituted [tex]x=\frac{1}{2}[/tex] into the equation and resulted with [tex]P(\frac{1}{2})=\frac{a-33}{4}[/tex]

    For b) I'm unsure what to do with the fact that I now have [tex]P(\frac{1}{2})=\frac{a-33}{4}[/tex] and [tex]P(-2)=17[/tex].

    A nudge in the right direction would be greatly appreciated :smile:
     
  2. jcsd
  3. Dec 12, 2008 #2
    P(-2) you will get another equation ^^
    except from P(-2)=17,
    however you are on the right track
     
  4. Dec 12, 2008 #3

    Mentallic

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    Oh wait I sub [tex]P(-2)[/tex] into the equation :grumpy:

    I really am that bad at polynomials that I keep missing these simple things!
     
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