1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Finding the remainder of an algebraic quotient

  1. Dec 7, 2014 #1
    I'm tutoring a pupil for a CLEP exam and her book includes the following algebra problem:
    What is the remainder when
    [tex]
    9x^{23} - 7x^{12} - 2x^{5} +1
    [/tex]
    is divided by [itex] x+1 [/itex]?
    I know how to find the answer by computing the quotient of these two expressions, but in this case doing that is so tedious I assume there's a more direct way of finding the remainder. What is it?

    Edit : I think this might be more appropriately placed in the "Homework and Coursework" section.
     
    Last edited: Dec 7, 2014
  2. jcsd
  3. Dec 7, 2014 #2
    Ruffini's rule speeds up the proces when divisior is in form "x-r"
     
  4. Dec 7, 2014 #3
    Indeed it does, thanks zoki85!
     
  5. Dec 8, 2014 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Since the problem is only to find the remainder, even simpler is "The remainder when dividing polynomial function P(x) by x- r is P(r)".
    That's easy to prove: let Q(x) be the quotient when P(x) is divided by x- r. The P(x)= Q(x)(x- r)+ remainder. Letting x= r give P(r)= Q(r)(0)+ remainder or "remainder= P(r)". To find the remainder when [itex]P(x)= 9x^{23}- 7x^{12}- 2x^5+ 1[/itex] is divided by x+1= x- (-1), just calculate
    [tex]P(-1)= 9(-1)^{23}- 7(-1)^{12}- 2(-1)^5+ 1[/tex].
     
    Last edited: Dec 8, 2014
  6. Dec 8, 2014 #5
    Wow! (high fives HallsofIvy)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Finding the remainder of an algebraic quotient
  1. Remainder theorem ? (Replies: 1)

  2. Graph of Remainders (Replies: 1)

Loading...