how do u tell if a polynomial is prime?

Answer 1

If it doesn't have any factors (of degree less than its own degree and more than 1) over the polynomial ring that it is defined.

If it is a polynomial of degree 2 or 3, you can check and see if it has any roots over the field that you are working.

A famous method of checking is Eisenstein's irreducibility criterion (for irreduciblity over the rationals):
Let f be your polynomial. If there exists some integer a and some prime p such that f(x-a)=(a_n)x^n+ . . . +(a_2)x^2+(a_1)x+a_0 where a_n≠0 (mod p), but a_(n-1)=a(n-2)= . . . = a_1 = a_0 = 0 (mod p) and a_0≠0 (mod p^2) then f is irreducible over the rationals.

(http://en.wikipedia.org/wiki/Eisenstein%27s_criterion )

Scuazmooq:
Checking for roots does not work in general:

(x^2+1)^2=x^4+2x^2+1 obviously doesn't have any roots, and obviously is reducible (over integers, rationals or reals).

Answer 2

I assume you mean non-factorable.

You can tell that if nothing can be factored from it. You'd have to use the quadratic equation or synthetic division (with the p/q solution set) to determine it for sure.

Answer 3

use a primality test