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How to factor this polynomial

  1. Dec 7, 2005 #1
    f(t) = t^3 - 6t^2 +9t + 2

    f(1) is not equal to 0
    f(-1) is not equal to 0
    f(2) is not equal to 0
    f(-2) is not equal to 0
    No common factor, can't group either

    How can I work this one out?
    thx
     
  2. jcsd
  3. Dec 7, 2005 #2

    Galileo

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    Here's something to remember.
    If f=a_0+a_1x+...+a_n x^n is a polynomial with integer coefficients of degree >=1 and q=b/c (ggd(b,c)=1) is a rational root, then b|a_0 and c|a_n.
    So the possible rational roots of your polynomial are [itex]\pm 2[/itex], which not roots. This means there are no rational roots so it's a nasty polynomial. :yuck:
     
  4. Dec 7, 2005 #3
    I don't believe this is factorable
     
  5. Dec 7, 2005 #4

    matt grime

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    Of course it's factorable, over some field, it's just that the roots aren't integers (or rational). There's even a formula for the roots. try googling for it.
     
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