# Need help with prime polynomial question!

• Sep 2nd 2009, 04:09 PM
ravensmom81
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!?!
• Sep 3rd 2009, 02:21 AM
Kiwi_Dave
Quote:

Originally Posted by ravensmom81
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.
• Sep 4th 2009, 04:07 AM
HallsofIvy
What is your definition of "prime polynomial"? Irreducible?