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Working on a polynomial

  1. Oct 21, 2008 #1
    1. The problem statement, all variables and given/known data

    when the polynomial f(x) is divided by (x-1) the remainder is 2, and when f(x) is divided by (x-3) the remainder is 4. Find the remainder when f(x) is divided by x2 - 4x + 3.


    3. The attempt at a solution

    i thought of adding the remainders since x2 - 4x + 3 = (x-1)(x-3) but that wouldn't sound very logical.....:S
     
  2. jcsd
  3. Oct 21, 2008 #2
    Re: polynomial!!!

    What is the degree of the remainder of f(x) divided by x2 - 4x + 3?
     
  4. Oct 21, 2008 #3
    Re: polynomial!!!

    ermm well it will be in the form (x + a)

    but how do i find a?
     
  5. Oct 22, 2008 #4
    Re: polynomial!!!

    While it is true in this case that the remainder is of the form x + a, I think it is usually the case that the remainder is in the form ax + b. How would you find this exactly? Well, consider that f(x) = (x-1)p(x) + 2 = (x-3)q(x) + 4 = (x-1)(x-3)s(x) + (ax+b). What do you get if you plug in f(1) and f(3)?
     
  6. Oct 22, 2008 #5
    Re: polynomial!!!

    i would get 2 equations for ax+b.

    then i'll be able to solve for a and b simultaneously......:)

    i hope this is correct.

    thnks
     
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