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Factorizationnof polynomilal

  1. Jan 27, 2006 #1
    Hello ,
    how to factorize the folowing polynomial[tex] X^4+X^3+X^2+X+1[/tex]
     
  2. jcsd
  3. Jan 27, 2006 #2

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    Multiply by (x-1).
     
  4. Jan 27, 2006 #3
    How please?
    can you clarify?
     
  5. Jan 27, 2006 #4

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    What do you mean how? Just multiply the polynomial by (x-1) and see what you get.
     
  6. Jan 27, 2006 #5
    So i need how factorize it in details
     
  7. Jan 27, 2006 #6

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    I'm not going to give you a step by step explanation of how to do this. That wouldn't really be helping you. Just try multiplying by (x-1). Do you not know how to do this? For example, if you had x2-x+1, multiplying by x-1 would give you (x-1)(x2-x+1) = x(x2-x+1)-(x2-x+1) = x3-x2+x-x2+x-1 = x3-2x2+2x-1.
     
  8. Jan 27, 2006 #7
    I Arrivided To X^5-1
    So How To Factorise It?
     
  9. Jan 27, 2006 #8

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    Are you familiar with compex numbers? How about the roots of unity? Try plugging in [itex]e^{i \theta}[/itex], and remember that a fifth degree polynomial has five roots. Also don't forget that 1 isn't really a root, since you multiplied by (x-1).
     
    Last edited: Jan 27, 2006
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