Homework Help Overview
The original poster seeks to find two polynomials of degree 2 in Z6[x] whose product results in a polynomial of degree 0. They also inquire whether the same can be achieved in Z7[x]. The context involves understanding polynomial degrees and the properties of polynomials over finite fields.
Discussion Character
- Exploratory, Assumption checking
Approaches and Questions Raised
- Participants discuss specific polynomial examples and their degrees, questioning the conditions under which the product of two degree 2 polynomials can yield a degree 0 polynomial. There is also exploration of the implications of working in Z6 versus Z7, particularly regarding zero divisors.
Discussion Status
Participants have raised relevant questions and provided insights about the nature of zero divisors in Z6 and Z7. The discussion is ongoing, with some clarity achieved regarding the differences between the two fields, but no consensus or resolution has been reached yet.
Contextual Notes
The original poster expresses confusion about the degree of the product of polynomials and the specific characteristics of Z6 and Z7, particularly regarding the presence of zero divisors in Z6.