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Homework Help: Finding value of polynomial using the remainder theorem

  1. Jun 30, 2010 #1
    1. The problem statement, all variables and given/known data

    Find the indicated value of the polynomial using the Remainder Theorem
    p(x)=2x^3-2x^2+11x-100; find p(3)

    2. Relevant equations

    p(x)=2x^3-2x^2+11x-100

    3. The attempt at a solution
    Synthetic division
    3] 2 -2 11 -100
    6 12 69
    2 4 23 [-31
    answer: p(3)=-31

    im not sure cuz i just followed the example in the book and applied it to this problem but the one in the book had another polynomial it was divided by to find the remainder. please help me, i have a test in the morning and im freaking out like crazy, thanks!!!
     
  2. jcsd
  3. Jun 30, 2010 #2

    HallsofIvy

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    Science Advisor

    Re: finding value of polynomial using the remainder theorem (check if answer is right

    Yes, that is correct. Esssentially what you have shown is that
    [tex]2x^3- 2x^2+ 11x- 100= (x- 3)(2x^2+ 4x+ 23)- 31[/tex]

    Putting x= 3 makes x- 3= 0 so whatever the number in the second paretheses is, the value is just -31.

    Certainly, it wouldn't have been that hard for you to check it yourself by evaluating directly: [itex]3^3= 27[/itex] so [itex]2(3^3)= 2(27)= 54[/itex]. [itex]-2(3^2)=-2(9)= -18[/itex]. 11(3)= 33 so the whole thing is 54- 18+ 33- 100= 36+ 33- 100= 69- 100= -31.
     
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