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Math Help - Need help with prime polynomial question!

  1. #1
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    Need help with prime polynomial question!

    Is it true that if the coefficients and exponents of a polynomial are all prime numbers, then the polynomial itself is a prime? I think that this statement is true, but I am not completely sure. It seem to me if these numbers are prime that they are factored completely, so the polynomial is prime. Would someone let me know if I am on the right track!?!
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  2. #2
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    Quote Originally Posted by ravensmom81 View Post
    Is it true that if the coefficients and exponents of a polynomial are all prime numbers, then the polynomial itself is a prime? I think that this statement is true, but I am not completely sure. It seem to me if these numbers are prime that they are factored completely, so the polynomial is prime. Would someone let me know if I am on the right track!?!
    Take the polynomial p=5x+3 when x is odd then p is even so p is not a prime.

    If the exponents must all be primes then there is no constant term because 0 is not prime meaning we are not allowed to have:

    p=...p_5x^5+p_3x^3+p_2x^2+p_0x^0

    and if there is no constant term then p is divisible by x.
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  3. #3
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    What is your definition of "prime polynomial"? Irreducible?
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