Talk:Discrete Mathematics/Polynomials

Wording
The introduction states "A polynomial over some commutative ring with identity R is an expression in the form". I first misread this as "commutative ring with (identity R)" rather than "(commutative ring with identity) [named] R". The context makes it pretty clear the latter is correct, but is there a better wording so that first timers don't make the same mistake I did? I'm still learning these subjects myself, but it seems commutative rings with identity are the norm so the "with identity" part could either be omitted or parenthesized.

Proving irreducibility
In showing that q(x)=x^4+x+2 is irreducible in Z_3, it's demonstrated that there are no linear factors by evaluating q(0), q(1), q(2), q(3), and q(4). However, since we're in Z_3, isn't evaluating q(3) and q(4) redundant with q(0) and q(1)?
 * good point Xiaodai 12:40, 12 November 2005 (UTC)

Division Algorithm
I beleive the line: Furthermore, we have the degree of r(x) ≤ degree of f(x) should read: Furthermore, we have the degree of r(x) ≤ degree of g(x)

I was going to say the same, only that the proper remark would be: ... the degree of r(x) < degree of g(x) The original statement might be right, but it's probably not as relevant as one regarding g(x). --Sgirbau (talk) 18:15, 8 December 2007 (UTC)