Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Solution Looking for a Problem

  1. Apr 23, 2012 #1
    While tutoring Algebra, division of polynomials, I ran across those problems with remainders. As an example: (x^2 + 2x + 1)/(x-7) the result is x + 9 with a remainder of 64/(x-7). I then assumed that the remainder was a positive integer and set x-7 equal to the divisors of 64 and solved for x.
    x - 7 = 1, x = 8 then the original polynomial became 64+16+1, or 81 of course is divisible by 1.
    x - 7 = 2, x = 9, 81+18+1 = 100, 2(50)
    x - 7 = 4, x = 11, 121+22+1 = 144, 4(36)
    x - 7 = 8, x = 15, 225+30+1 = 256, 8(32)
    x - 7 = 16, x = 23, 529+46+1 = 576, 16(36)
    x - 7 = 32, x = 39, 1521+78+1 = 1600, 32(50)
    x - 7 = 64, x = 71, 5041+142+1 = 5184, 64(81)

    I thought this was interesting, however, I could not think of a problem where I could apply this solution. It may work for solving for different bases, etc.
     
  2. jcsd
  3. Jun 8, 2012 #2
    This is tricky method to solve, yes definitely this method is going to use to find the value of X, this is sort cut method to solve this problem of finding the value of x
     
  4. Jun 8, 2012 #3
    You would get similar results if you chose x - 2^n + 1 in lieu of x - 7. Or try other negative prime powers plus 1.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook