Results 1 to 2 of 2

Thread: Remainder Theorem

  1. #1
    Newbie
    Joined
    Oct 2008
    Posts
    20

    Remainder Theorem

    Use the remainder theorem to factorise :

    1) x^3 +3x^2 - 4

    2) x^4 + 3x^3 + 5x^2 + 9x + 6
    Follow Math Help Forum on Facebook and Google+

  2. #2
    A riddle wrapped in an enigma
    masters's Avatar
    Joined
    Jan 2008
    From
    Big Stone Gap, Virginia
    Posts
    2,550
    Thanks
    15
    Awards
    1
    Quote Originally Posted by Jen1603 View Post
    Use the remainder theorem to factorise :

    1) $\displaystyle f(x)=x^3 +3x^2 - 4$
    The rational roots theorem tells us if this has rational roots, they will be
    $\displaystyle \pm 1, \pm 2, \pm4$

    Test each one using the remainder theorem to see which one(s) satisfy $\displaystyle f(x)=0$

    I found $\displaystyle f(-2)=0$, so $\displaystyle x+2$ is a factor.

    To find the remaining factors, you could test the rest of the possible rational roots using the remainder theorem or use synthetic division with divisor -2to reduce the polynomal to a quadratic that you can factor.

    Code:
     
    -2 | 1  3   0  -4
           -2  -2   4
        ------------
         1  1  -2  0
    The quadratic remaining after factoring $\displaystyle x+2$ is $\displaystyle x^2+x-2$

    That factors into $\displaystyle (x+2)(x-1)$

    $\displaystyle \boxed{f(x)=(x+2)(x+2)(x-1)}$

    Quote Originally Posted by Jen1603 View Post
    2)$\displaystyle f(x)= x^4 + 3x^3 + 5x^2 + 9x + 6$
    Test these factors $\displaystyle \pm 1, \pm 2, \pm 3, \pm 6$

    There are no sign changes in this polynomial, so no need to check for positive zero because there aren't any (Descartes Rule of Signs)
    Last edited by masters; Nov 3rd 2008 at 01:28 PM.
    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: Oct 9th 2010, 01:29 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: 5
    Last Post: Jul 19th 2009, 02:08 PM
  4. remainder theorem
    Posted in the Algebra Forum
    Replies: 1
    Last Post: Mar 9th 2009, 01:16 PM
  5. Factor Theorem and Remainder Theorem
    Posted in the Algebra Forum
    Replies: 2
    Last Post: Sep 8th 2007, 10:50 AM

Search Tags


/mathhelpforum @mathhelpforum