(a) Prove that (x - I) I I(x) in Z2[X] iff I(x) has an even number of nonzero
Chapter 36, Problem 36.19(choose chapter or problem)
(a) Prove that (x - I) I I(x) in Z2[X] iff I(x) has an even number of nonzero coefficients.(b) Prove that if deg I(x) > 1 and I(x) is irreducible over Z2, then I(x) has constant termI and an odd number of nonzero coefficients.(c) Determine all irreducible polynomials of degree 4 or less over Z2.(d) Write each polynomial of degree 3 over Z2 as a product of irreducible factors.
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