Results 1 to 2 of 2

Thread: Remainder & Factor Thm

  1. #1
    Member
    Joined
    Oct 2006
    Posts
    206
    Thanks
    1

    Remainder & Factor Thm

    The expression $\displaystyle g(x)$ has the same remainder constant $\displaystyle k$ when divided by $\displaystyle (x-a)$ or $\displaystyle (x-b)$. Determine, with reasons, whether it is always true that $\displaystyle g(x)$ also has remainder constant $\displaystyle k$ when divided by $\displaystyle (x-a)(x-b), k \neq 0$.

    My proof:

    $\displaystyle g(x)=(x-a)Q_{1}(x)+k$
    $\displaystyle g(x)=(x-b)Q_{2}(x)+k$

    where $\displaystyle Q_{1}(x)$ and $\displaystyle Q_{2}(x)$ are quotients.

    Let $\displaystyle f(x)=g(x)-k$,
    then $\displaystyle f(x)=(x-a)Q_{1}(x)$ and $\displaystyle f(x)=(x-b)Q_{2}(x)$.

    So $\displaystyle (x-a)$ and $\displaystyle (x-b)$ are factors of $\displaystyle f(x)$

    Thus,
    $\displaystyle f(x)=(x-a)(x-b)Q_{3}(x)$
    $\displaystyle \Rightarrow g(x)-k=(x-a)(x-b)Q_{3}(x)$
    $\displaystyle \Rightarrow g(x)=(x-a)(x-b)Q_{3}(x)+k$

    Hence, it is TRUE.

    Is my proof ok? Is there a better one?
    Many thanks for those who help
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
    Joined
    Mar 2008
    From
    P(I'm here)=1/3, P(I'm there)=t+1/3
    Posts
    5,618
    Thanks
    6
    Hello,

    Your proof is ok
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Factor/Remainder theorem
    Posted in the Algebra Forum
    Replies: 7
    Last Post: Dec 2nd 2009, 04:27 AM
  2. remainder & factor theorem
    Posted in the Algebra Forum
    Replies: 4
    Last Post: Jul 24th 2009, 07:17 AM
  3. Factor and remainder theorem
    Posted in the Algebra Forum
    Replies: 0
    Last Post: Jun 27th 2009, 11:47 PM
  4. The remainder and factor theorems
    Posted in the Algebra Forum
    Replies: 7
    Last Post: Apr 7th 2009, 04:45 PM
  5. Remainder and Factor Theorem HELP
    Posted in the Algebra Forum
    Replies: 1
    Last Post: Nov 20th 2008, 12:37 PM

Search Tags


/mathhelpforum @mathhelpforum