Results 1 to 4 of 4

Math Help - Factoring polynomials

  1. #1
    Newbie
    Joined
    Mar 2011
    Posts
    1

    Factoring polynomials

    Please forgive me for any placement errors of the thread or ah..pretty much any errors here. Being new and all I feel a bit intimidated here.

    Anyway, as the topic says I'm currently stuck with factoring some polynomials. We're given one factor and we have to find the rest. Process is through synthetic substitution.

    3x^ - 4x^ - 17x + 6; x + 2
    Now, I can work through most problems dealing with this. But what I'm stuck on...is the very first number. Does it effect the outcome of the problem at all? Anything you should do with it before attempting to solve or do you just go through with it and mess with it at the end?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member TheChaz's Avatar
    Joined
    Nov 2010
    From
    Northwest Arkansas
    Posts
    600
    Thanks
    2
    When given a factor (such as x + 2), set it equal to zero.
    Then we will have x = -2. This is the number that goes "in the box" when doing synthetic division.

    There's no way I'm going to try to visually reproduce the process (!), so I'll just talk you through it...
    Your coefficients are 3, -4, -17, and 6.

    Bring down the
    3. Then 3*-2 + -4 =
    -10. Then -10*-2 + -17 =
    3. Then 3*-2 + 6 = 0 (as it should).

    You now have coefficients 3, -10, and 3, corresponding to the quadratic

    3x^2 - 10x + 3

    Now you can factor this into (3x - 1)(x - 3), but don't lose the original factor!

    Your full factorization is (3x - 1)(x - 3)(x + 2)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Apr 2009
    Posts
    8
    You can just work through it normally:

    Using synthetic division: h=-2 as (x+2) is a factor (write the coefficients, drop the first, multiply up by 'h' and then add down the next column etc)

    3 -4 -17 6
    + -6 -20 6
    3 -10 3 0

    This will leave you with 3x^2-10x+3 as the result of the first factorization and then factoring that can be done by breaking that into 3x^2 -9x-1x+3 = 3x(x-3)-1(x-3) = (3x-1)(x-3)

    This gives you the three factors of (x+2)(3x-1)(x-3)
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member TheChaz's Avatar
    Joined
    Nov 2010
    From
    Northwest Arkansas
    Posts
    600
    Thanks
    2
    Quote Originally Posted by Mahanen View Post
    ...

    3 -4 -17 6
    + -6 -20 6
    3 -10 3 0
    ...
    I guess that wasn't so bad!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Factoring Polynomials Help
    Posted in the Algebra Forum
    Replies: 1
    Last Post: January 13th 2010, 05:47 PM
  2. factoring polynomials
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: September 20th 2009, 02:05 AM
  3. Replies: 2
    Last Post: August 22nd 2009, 11:57 AM
  4. Factoring Polynomials
    Posted in the Algebra Forum
    Replies: 5
    Last Post: January 10th 2009, 02:03 PM
  5. Replies: 5
    Last Post: November 29th 2005, 04:22 PM

Search Tags


/mathhelpforum @mathhelpforum