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Linear Algebra Dimension theorem to prove a polynomial can written in a certain way

  1. Mar 14, 2012 #1
    Use the dimension theorem to show that every polynomial p(x) in Pn can be written in the form p(x)=q(x+1)-q(x) for some polynomial q(x) in Pn+1.

    I need to see all the steps so that I understand how to do it.
    PLease and Thank you
     
  2. jcsd
  3. Mar 14, 2012 #2

    SammyS

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    Re: Linear Algebra Dimension theorem to prove a polynomial can written in a certain w

    Hello linalg. Welcome to PF !

    What have you tried ?

    Where are you stuck?


    Please look at the rules for this Forum. We won't do your work for you but will try tu help you arrive the solution.
     
  4. Mar 15, 2012 #3
    Re: Linear Algebra Dimension theorem to prove a polynomial can written in a certain w

    I am actually very confused on where to start. I tried poving if it is linear independent and then kinda got lost.
    Please help
     
  5. Mar 15, 2012 #4

    Ray Vickson

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    Re: Linear Algebra Dimension theorem to prove a polynomial can written in a certain w

    Try the cases n=1 and n=2 first. That will show you what to do in general.

    RGV
     
  6. Mar 15, 2012 #5
    Re: Linear Algebra Dimension theorem to prove a polynomial can written in a certain w

    Thanks for your guys' help. I tried the two cases n=1 and n=2 but i am still lost. Its a homework question due tomorrow that I don't need to understand how to do it until the test in a couple weeks.
     
  7. Mar 15, 2012 #6

    Ray Vickson

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    Re: Linear Algebra Dimension theorem to prove a polynomial can written in a certain w

    If q(x) is a polynomial of degree 2, is h(x) = q(x+1) a polynomial in x? What is its degree? What are its x-coefficients?

    RGV
     
  8. Mar 15, 2012 #7

    Mark44

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    Re: Linear Algebra Dimension theorem to prove a polynomial can written in a certain w

    This isn't how it words here at Physics Forums.
     
  9. Mar 15, 2012 #8
    Re: Linear Algebra Dimension theorem to prove a polynomial can written in a certain w

    Ok Mark44 just answer the question then
     
  10. Mar 15, 2012 #9

    Mark44

    Staff: Mentor

    Re: Linear Algebra Dimension theorem to prove a polynomial can written in a certain w

    What question? You have not asked a single question.
     
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