# reducible

1. ### solving (x+a)^2 d2y/dx2 -4(x+a) dy/dx + 6y = x

Hi, my question is that can we find the particular integral of this kind of equation by variation of parameters? If yes, then what mistake did I make in my solution in the provided link? If this is not the method to adopt, what other method can we use?
2. ### Irreducible or reducible polynomial?

Hi all, I have used rational root test and obtain this result for the question: f(x) = 2x^4+8x^3+5x^2âˆ’7xâˆ’3=(2x^2+2xâˆ’3)(x^2+3x+1) This shows that there is no linear factor but a quadratic factors instead. Do I still consider such polynomial as reducible or irreducible? Am I...
3. ### Why is $2x^2 + 4$ reducible over Z but not Q?

We can rewrite $2x^2 +4$ as $2(x^2 + 2)$ so wouldnt this polynomial be reducible over both $\mathbb{Z}$ and $\mathbb{Q}$?
4. ### Root of a reducible polynomial

Hey guys, just took an exam it completely kicked my ass. This was one of the problems that I could just not make any headway on: Suppose F is a field of characteristic p > 0 and let f(x)=x^p-a \in F[x] for some a \not= 0. Further suppose there is a field E containing F such that we have \alpha...
5. ### Equations Reducible to Quadratics-Substitution

Solve equation: z = 8?z + 240 I set it equal to zero: -z + 8?z = 0 Normally I would substitute the ?z for another variable to make it into a quadratic formula, then solve from there, but the z is negative so i'm not sure how to go about this... Thanks
6. ### factorising reducible polynomials

Basically, I am doing some cryptography, I need to show that a polynomial I have, which is not irreducible, implies it is not primitive. I am having trouble factorising these rather large polynomials. I have checked to see whether the following polynomials are irreducible and found their...