Question

omialS 1. (a)Tell why the polynomial +22 must be irreducible over the rational numbers. (b) What does this mean about the field EQ/r3 2 +3)? (c) What is a basis for this field, considered as a field extensions of its field of constants, isomorphic to Q? (d) What is the degree of the extension E:Q? (e) Let y denote the equivalence class of z in E. Add and multiply these two elements of E: 1 + 2y + y2,y-Zy2 and express the results as quadratic olynomials in y.

Answer 1

be a poly no mial and a Z, iat p be ony pyma such +823 y"--ay-sy2 we hare Using y"--2-24 ,