Results 1 to 3 of 3

Math Help - remainder theorem issue

  1. #1
    Senior Member
    Joined
    Jul 2010
    Posts
    358
    Thanks
    4

    remainder theorem issue

    Hi;
    When using the remainder theorem do I always plug the root in?
    If yes why?

    ie dividing by (x - 1) plud in a 1 and (x + 1) plug in -1
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,401
    Thanks
    1273

    Re: remainder theorem issue

    Quote Originally Posted by anthonye View Post
    Hi;
    When using the remainder theorem do I always plug the root in?
    If yes why?

    ie dividing by (x - 1) plud in a 1 and (x + 1) plug in -1
    If you divide a polynomial \displaystyle \begin{align*} P(x) \end{align*} by \displaystyle \begin{align*} ax + b \end{align*}, you will get a quotient of one less degree plus a remainder with a constant numerator. So

    \displaystyle \begin{align*} \frac{P(x)}{ax + b} &= Q(x) + \frac{R}{ax + b} \\ P(x) &= (ax + b)Q(x) + R  \end{align*}

    Now if you let \displaystyle \begin{align*} x = -\frac{b}{a} \end{align*}, you have \displaystyle \begin{align*} ax + b = 0 \end{align*}, so

    \displaystyle \begin{align*} P\left(-\frac{b}{a}\right) &= 0\,Q\left(-\frac{b}{a}\right) + R \\ P\left(-\frac{b}{a}\right) &= R \end{align*}

    So yes, when you want to find the remainder when dividing a polynomial by \displaystyle \begin{align*} ax + b \end{align*}, you plug in \displaystyle \begin{align*} -\frac{b}{a} \end{align*}.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Jul 2010
    Posts
    358
    Thanks
    4

    Re: remainder theorem issue

    Thank you.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. remainder theorem
    Posted in the Algebra Forum
    Replies: 3
    Last Post: September 17th 2009, 05:26 AM
  2. Remainder Theorem
    Posted in the Algebra Forum
    Replies: 4
    Last Post: July 26th 2009, 08:05 PM
  3. remainder theorem
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: January 5th 2009, 05:24 AM
  4. Factor Theorem and Remainder Theorem
    Posted in the Algebra Forum
    Replies: 2
    Last Post: September 8th 2007, 10:50 AM
  5. Remainder Theorem
    Posted in the Algebra Forum
    Replies: 6
    Last Post: March 21st 2007, 02:14 AM

Search Tags


/mathhelpforum @mathhelpforum