Originally Posted by
Coda202 Show that there is only one way (disregarding the order of the factors) to factor x^2 +x+3 as a product of monic irreducible polynomials in Z(sub5)[x].
So, I found that f(1) produces a zero for this polynomial, then I used to the division algorithm to get (x^2 +x+3)/(x-1) = (x+2). However, (x-1)(x+2) does not equal x^2 +x+3, so now I am stuck...
I also used the quadratic formula to get a pair of complex roots, but I'm unsure as how to prove that is the only way to factor x^2 +x+3 as a product of irreducible monic polynomials in Z(sub5)[z]