Results 1 to 7 of 7

Math Help - Factor 2x^3 - 3x + 1

  1. #1
    Newbie
    Joined
    Jun 2012
    From
    US
    Posts
    9

    Factor 2x^3 - 3x + 1

    Please show me how to factor 2x^3 - 3x + 1

    Thanks in advance!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Mar 2012
    From
    Sheffield England
    Posts
    440
    Thanks
    76

    Re: Factor 2x^3 - 3x + 1

    Quote Originally Posted by Roleparadise View Post
    Please show me how to factor 2x^3 - 3x + 1

    Thanks in advance!
    It is easy to see that expression =0 when x=1 It follows that x-1 is a factor. The 2nd bracket then must begin with 2x^2 and end in -1
    SO 2x^3-3x+1= (x-1)(2x^2 _1) Multiplying these out as they are would give a term -2x^2 which we dont want. Putting =2x in the middle of the 2nd bracket will get rid of this. So 2x^3-3x+1=(x-1)(2x^2+2x-1) Notice this also gives us the required -3x term.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jun 2012
    From
    US
    Posts
    9

    Re: Factor 2x^3 - 3x + 1

    Thank you, but I was wanting to break it into three roots. The term being factored is a derivative for which I am trying to find the critical values. I got as far as you did but was not able to break it down further. Feel free to speak in calculus terms; what do I do next?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member
    Joined
    Mar 2012
    From
    Sheffield England
    Posts
    440
    Thanks
    76

    Re: Factor 2x^3 - 3x + 1

    Quote Originally Posted by Roleparadise View Post
    Please show me how to factor 2x^3 - 3x + 1

    Thanks in advance!
    Following on from my earlier post the 2nd bracket breaks down to (2x+1)(x-1) so final answer is
    2x^3-3x+1= (x-1)(2x+1)(x-1)=(2x+1)(x-1)^2
    Last edited by biffboy; June 18th 2012 at 05:06 AM. Reason: mistake in it
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Jun 2012
    From
    US
    Posts
    9

    Re: Factor 2x^3 - 3x + 1

    How did you get that 2x^2+2x-1 breaks down to (2x+1)(x-1) ? When I multiply them together I reach 2x^2-x-1, not 2x^2+2x-1
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member Goku's Avatar
    Joined
    Mar 2011
    From
    South Africa
    Posts
    84
    Thanks
    10

    Re: Factor 2x^3 - 3x + 1

    You will have to use the Quadratic formula, to find the factors, because 2x^2+2x-1 cannot be factored into integers.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,715
    Thanks
    1642
    Awards
    1

    Re: Factor 2x^3 - 3x + 1

    Quote Originally Posted by Roleparadise View Post
    Please show me how to factor 2x^3 - 3x + 1
    \left( {x - 1} \right)\left( {x - \left[ {\frac{{ - 1}}{2} + \frac{{\sqrt 3 }}{2}} \right]} \right)\left( {x - \left[ {\frac{{ - 1}}{2} - \frac{{\sqrt 3 }}{2}} \right]} \right)
    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. how could i factor this
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: February 10th 2010, 02:28 AM
  5. cannot factor y^2-3y-4
    Posted in the Algebra Forum
    Replies: 5
    Last Post: May 17th 2009, 10:46 AM

Search Tags


/mathhelpforum @mathhelpforum