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Remainder Theorem with 2 unknowns.

  1. Feb 22, 2008 #1
    1. The problem statement, all variables and given/known data
    When rx^3 + gx^2 +4x + 1 is divided by x-1, the remainder is 12. When it is divided by x+3, the remainder is -20. Find the values of r and g.

    2. Relevant equations



    3. The attempt at a solution
    r=f(1)
    =r(1)^3 + g(1)^2 + 4(1) +5
    =r + g +9
    r=12
    r+g+9=12
    r+g= 3

    r=f(-3)
    =r(-3)^3 + g(-3)^2 + 4(-3) +5
    =-27r +9g -7
    r=-20
    -27r +9g -7=-20
    -27 +9g=-13

    Then I was just going to use elimination to find r and g.
    -27r-27g=-81 (equation 1 multiplied by -27)
    -27r+9g=-13
    -------------
    -36g=-68
    g= 1.89

    But that answer is wrong.
    Is one of my equations wrong or am I going about it incorrectly?
    I was able to find the unknown in a equation similar to this, so I'm not sure why I'm having such trouble with this one.
    Thanks for any help!
     
  2. jcsd
  3. Feb 22, 2008 #2

    NateTG

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    Science Advisor
    Homework Helper

    Where did the 5 come from?

    NB:
    It's probably a bad idea to use 'r' as your remainder as well as one of the unknowns.
    Might be written better as:
    Code (Text):

    12=f(1)
    12=(1)^3r+(1)^2g+(1)4+5
    12=1r+1g+4+5
    12=r+g+9
     3=r+g
     

    Also, this bit is correct:
    But IMHO this is much more legible.
    Code (Text):

     27r+27g= 81
    -27r+ 9g=-13
    ------------------
      0r+36g= 68
     
     
    Last edited: Feb 22, 2008
  4. Feb 22, 2008 #3
    Oh wow, you're completely right.
    I think I just wrote the equation wrong in my notes, but when I posted this I read the equation from the textbook. Hahah, well, thanks!
     
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