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Math Help - polynomials

  1. March 30th 2009, 01:07 PM #1
    sidi
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    polynomials

    I have one more problem...
    I want to find all rings Zn, such the polynomial x+2 divides polynomial (x^5)-10x+12.
    Could anybody help me?
    Thanks, this is a new topic for me...
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  2. March 30th 2009, 01:49 PM #2
    NonCommAlg
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    Quote Originally Posted by sidi View Post

    I have one more problem...
    I want to find all rings Zn, such the polynomial x+2 divides polynomial (x^5)-10x+12.
    Could anybody help me?
    Thanks, this is a new topic for me...
    x^5 - 10x + 12 is divisible by x+2 in any (unitary) ring because (-2)^5 -10 \times (-2) + 12 = \text{what} ?
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  3. March 31st 2009, 02:46 PM #3
    sidi
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    of course, -2 is root of that polynomial...I know. I think it should work, that it is divisible in any ring, but I canīt find the reason...
    Zn isnīt a subring of Z, or am I wrong??
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  4. March 31st 2009, 03:41 PM #4
    NonCommAlg
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    Quote Originally Posted by sidi View Post

    Zn isnīt a subring of Z, or am I wrong??
    no, it's not a subring of Z.
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  5. March 31st 2009, 03:53 PM #5
    sidi
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    can you give me one more hint please? I am really trying to find out why it is so in any ring, but Iīm afraid Iīm not able to do it now. I have passed an exam (not algebra) few hours ago, Iīm exhausted, but I really want to do my homework...
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