Show that f(x) = x^3 + x + 1 is irreducible over Z2[x]

Construct the addition and multiplication tables for Z2[x]/(f) **If I knew the elements I could do this

Find a cyclic generator for the multiplicative group.

Any help please?

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- Nov 25th 2012, 07:44 PMTimsBobby2Show that f(x) is irreducible, cyclic generator,...
Show that f(x) = x^3 + x + 1 is irreducible over Z2[x]

Construct the addition and multiplication tables for Z2[x]/(f) **If I knew the elements I could do this

Find a cyclic generator for the multiplicative group.

Any help please?