1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

How to factor x^3 - 4x + 4

  1. Dec 8, 2008 #1
    1. The problem statement, all variables and given/known data
    [tex]x^3-4x+4[/tex]


    2. Relevant equations
    None


    3. The attempt at a solution
    I tried using the quadratic formula but it doesnt work. I started with this, but I don't know what to do now.[tex]x^{3}+0x^2-4x+4[/tex]
     
  2. jcsd
  3. Dec 8, 2008 #2

    gabbagabbahey

    User Avatar
    Homework Helper
    Gold Member

    Re: Factoring

    What exactly are you trying to do?!

    [itex]x^3-4x+4[/itex] is an expression, not a problem statement! Do you mean that you are trying to find the roots of the equation [itex]x^3-4x+4=0[/itex]?
     
  4. Dec 8, 2008 #3
    Re: Factoring

    yes I am trying to find the roots of the equation
     
  5. Dec 8, 2008 #4

    gabbagabbahey

    User Avatar
    Homework Helper
    Gold Member

    Re: Factoring

    Well, there are no simple solutions to this cubic equation. You can try using the cubic formula found here.

    Is this the entire question, or is this part of a larger problem? Are you sure you have have written the equation correctly?
     
  6. Dec 8, 2008 #5
    Re: Factoring

    This is the correct equation, and it is the entire question.
     
  7. Dec 8, 2008 #6

    gabbagabbahey

    User Avatar
    Homework Helper
    Gold Member

    Re: Factoring

    Are you asked to use any specific method? (such as approximating the real root using newton's method)
    Are you allowed to use a calculator/computer?
     
  8. Dec 8, 2008 #7
    Re: Factoring

    No specific method is being asked but you can use a simple scientific calculator.
     
  9. Dec 8, 2008 #8

    gabbagabbahey

    User Avatar
    Homework Helper
    Gold Member

    Re: Factoring

    What methods have you been taught in whichever course this is for? Use one of those.
     
  10. Dec 8, 2008 #9
    Re: Factoring

    Edit~
     
  11. Dec 8, 2008 #10

    gabbagabbahey

    User Avatar
    Homework Helper
    Gold Member

    Re: Factoring

    There are no rational roots to this equation, so that method won't work.
     
  12. Dec 9, 2008 #11
    Re: Factoring

    Find the roots using Cardano's method.

    [tex]D=(\frac{4}{2})^2 + (\frac{-4}{3})^3=4 - \frac{64}{27}=\frac{108-64}{27}=\frac{44}{27} > 0[/tex], so it got one rational and two complex roots.

    The rational one is ~(-2.38)
     
  13. Dec 9, 2008 #12

    gabbagabbahey

    User Avatar
    Homework Helper
    Gold Member

    Re: Factoring

    The root (-2.38) is real not rational. The rational roots theorem tells you that the only possible candidates for rational roots of this equation are [itex]\pm 1[/itex], [itex]\pm 2[/itex], and [itex]\pm 4[/itex]....and since none of these are roots; there are no rational roots.
     
  14. Dec 10, 2008 #13
    Re: Factoring

    Rational numbers are also real numbers. So I suppose -2.38....(infinite number of decimals) is irrational number (also real number).
     
  15. Dec 10, 2008 #14

    gabbagabbahey

    User Avatar
    Homework Helper
    Gold Member

    Re: Factoring

    A rational number is a real number that can be expressed as a ratio of two integers....for example, 1/3, 0.25, and 3658793659/548709568017097 are rational numbers.

    However, things like [itex]\pi[/itex], [itex]\sqrt{2}[/itex] and any non-repeating non-terminating decimal are irrational numbers.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: How to factor x^3 - 4x + 4
  1. X^4 - x^3 (Replies: 4)

  2. Factoring (X^4+1) (Replies: 3)

Loading...