Results 1 to 7 of 7

Math Help - Factoring polynomial degree 4

  1. #1
    Newbie
    Joined
    Feb 2009
    Posts
    2

    Factoring polynomial degree 4

    Show that x = -2.22 is a solution for:

    2.00 x4 - 3.00x3 +5.00x = 70.0

    When using a calculator I get 70.3. I have been unable to factor the equation so Iím wondering is this a solution obtained by a graph or is there a factoring method that will lead to this solution?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Dec 2008
    From
    Scotland
    Posts
    901
    Quote Originally Posted by wrjones View Post
    Show that x = -2.22 is a solution for:

    2.00 x4 - 3.00x3 +5.00x = 70.0

    When using a calculator I get 70.3. I have been unable to factor the equation so Iím wondering is this a solution obtained by a graph or is there a factoring method that will lead to this solution?
    If the question is simply to show that x = -2.22 is a factor, then I suggest you use long/synthetic division to show that (x+2.22) divides into  2x^4 -3x^3 + 5x - 70 without a remainder!
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Feb 2009
    Posts
    2

    factor

    Thanks for looking at the problem. It seems that by the fact I'm off by a half percent when just plugging in the number that there would be a remainder but I guess I will give it a try.

    Thanks for looking at the problem.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,952
    Thanks
    1629
    You are completely right. x= -2.22 does NOT satisfy that equation.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member
    Joined
    Dec 2008
    From
    Scotland
    Posts
    901
    Quote Originally Posted by HallsofIvy View Post
    You are completely right. x= -2.22 does NOT satisfy that equation.
    No, but the solutions to the equations are irrational, and the result x = -2.22 is a rounded effort.

    The remainder is small enough to be neglected for all intents and purposes, imo.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor Reckoner's Avatar
    Joined
    May 2008
    From
    Baltimore, MD (USA)
    Posts
    1,024
    Thanks
    75
    Awards
    1

    Smile

    Quote Originally Posted by wrjones View Post
    Show that x = -2.22 is a solution for:

    2.00 x4 - 3.00x3 +5.00x = 70.0

    When using a calculator I get 70.3. I have been unable to factor the equation so I’m wondering is this a solution obtained by a graph or is there a factoring method that will lead to this solution?
    As others said, the discrepancy is due to rounding.

    None of the roots are rational, and although I was able to get an exact solution with CAS software, it was several pages' worth of radicals and fractions, so I think a numerical approximation works best here.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by wrjones View Post
    Show that x = -2.22 is a solution for:

    2.00 x4 - 3.00x3 +5.00x = 70.0

    When using a calculator I get 70.3. I have been unable to factor the equation so Iím wondering is this a solution obtained by a graph or is there a factoring method that will lead to this solution?
    Only if rounded to two decimal places is -2.22 a solution to this, but such precision is not acceptable unless the question asks for it, which may be the case as the coefficients are given to two decimal places.

    CB
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 4
    Last Post: April 7th 2011, 10:08 AM
  2. factoring 4th degree polynomials
    Posted in the Algebra Forum
    Replies: 6
    Last Post: February 8th 2011, 11:32 AM
  3. Factoring A Third Degree Polynomial
    Posted in the Algebra Forum
    Replies: 8
    Last Post: January 24th 2011, 07:12 PM
  4. Factoring 3rd degree polynomials
    Posted in the Pre-Calculus Forum
    Replies: 6
    Last Post: December 6th 2010, 12:24 PM
  5. (Year 10) Factoring 6th Degree Polynomial
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: October 1st 2008, 02:07 PM

Search Tags


/mathhelpforum @mathhelpforum