Results 1 to 5 of 5

Math Help - Which of the following is a factor of

  1. #1
    Newbie
    Joined
    Jun 2010
    Posts
    5

    Which of the following is a factor of

    Which of the following is a factor of?

    P(x) = x^4+ 6x^3+ 9x^2+ 3x + 9 ?


    a) x - 2
    b) x + 2
    c) x + 3
    d) x - 3
    e) None of the above
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,522
    Thanks
    1405
    Use the Factor Theorem, namely that for any Polynomial function P(x), if P(a) = 0 then x - a is a factor.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jun 2010
    Posts
    5
    the answer is x+3

    P(x) = (-3)^4+ 6x^(-3)+ 9(-3)^2+ 3(-3) + 9= 0

    ?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,522
    Thanks
    1405
    Quote Originally Posted by dragovx View Post
    the answer is x+3

    P(x) = (-3)^4+ 6x^(-3)+ 9(-3)^2+ 3(-3) + 9= 0

    ?
    You're on the right track.

    If you're testing x + 3 as a factor, then P(-3) = 0...


    P(x) = x^4 + 6x^3 + 9x^2 + 3x + 9

    P(-3) = (-3)^4 + 6(-3)^3 + 9(-3)^2 + 3(-3) + 9

     = 81 + 6(-27) + 9(9) - 9 + 9

     = 81 - 162 + 81 - 9 + 9

     = 0 as required.


    Therefore x + 3 is a factor.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by dragovx View Post
    Which of the following is a factor of?

    P(x) = x^4+ 6x^3+ 9x^2+ 3x + 9 ?


    a) x - 2
    b) x + 2
    c) x + 3
    d) x - 3
    e) None of the above
    The rational roots theorem allows the first two to be eliminated with no further consideration and Descartes rule of signs tell you that this has no positive roots which eliminates x-3 leaving only one case to check.

    CB
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: July 19th 2011, 11:45 AM
  2. factor analysis , extract second factor loading
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: June 1st 2011, 05:17 AM
  3. factor analysis , extract second factor loading
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: May 30th 2011, 05:29 AM
  4. Factor 3x^2 +2x -6
    Posted in the Algebra Forum
    Replies: 8
    Last Post: October 11th 2009, 10:12 AM
  5. How do i factor this?
    Posted in the Algebra Forum
    Replies: 4
    Last Post: September 18th 2008, 02:45 PM

Search Tags


/mathhelpforum @mathhelpforum