Results 1 to 3 of 3

Thread: remainder theorem issue

  1. #1
    Super Member
    Joined
    Jul 2010
    Posts
    595
    Thanks
    5

    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
    12,880
    Thanks
    1946

    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 $\displaystyle \displaystyle \begin{align*} P(x) \end{align*}$ by $\displaystyle \displaystyle \begin{align*} ax + b \end{align*}$, you will get a quotient of one less degree plus a remainder with a constant numerator. So

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

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

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

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

  3. #3
    Super Member
    Joined
    Jul 2010
    Posts
    595
    Thanks
    5

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

Search Tags


/mathhelpforum @mathhelpforum