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Factoring polynomials

  1. Sep 30, 2012 #1
    z^4-4z^3+6z^2-4z-15 =0

    How can i factor this polynomial in order to find the solutions??


    I tried with the ruffini' rule.

    and i reached the following equation [(z+1)(-z^3-5z^2+11z-15)] =0

    now how can i factor (-z^3-5z^2+11z-15) ???

    i tried it, but i can not solve it... :/
     
  2. jcsd
  3. Sep 30, 2012 #2
    Proceed with Ruffini. You'll find another root (because the problem is easy) and the remaining factor is quadratic, whose solutions you get with the formula.
     
  4. Sep 30, 2012 #3
    the solutions are

    -1; 3; 1+/-2i

    i am going to try with ruffini again.
     
  5. Sep 30, 2012 #4
    i cant. Even knowing the solutions, i can not proceed with ruffini's rule.
    Maybe something is escaping me.
     
  6. Sep 30, 2012 #5
    Redo the quotient (z^4-4z^3+6z^2-4z-15)/(z+1), since the leading term must be z^3, not -z^3.
     
  7. Sep 30, 2012 #6
    ok it now makes sense.

    now i factor it


    (z^3-5z^2+11z-15)/(z-3)



    ...

    but without the solution i would never be able to discover that i should divide (z^3-5z^2+11z-15) by (z-3)
     
  8. Sep 30, 2012 #7
    Do Ruffini again: try with the divisors of -15 of both signs.
     
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