a. Show that x 3 + x 2 + 1 is irreducible over Z 2 . b.
Question:
a. Show that x3 + x2 + 1 is irreducible over Z2.
b. Let a be a zero of x3 + x2 + 1 in an extension field of Z2. Show that x3 + x2 + 1 factors into three linear factors in (Z2(α))[x] by actually finding this factorization.
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a Let fx x 3 x 2 1 Then f0 1 and f1 1 so fx has no zeros in Z 2 and is thus irreducible ...View the full answer
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