4. Show that the polynomial g(x) = x+x+1 is irreducible over Z2. In the quotient ring...

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4. Show that the polynomial g(x) = x+x+1 is irreducible over Z2. In the quotient ring Z2[r]/(g(x)) let d = x+(g(x)), so that Z2[2]/(g(x)) = Z2(8). Express 8 and (82 + 1)-1 in the form a + b8 + co² + d8³, where a, b, c, d e Z2. 4. Show that the polynomial g(x) = x+x+1 is irreducible over Z2. In the quotient ring Z2[r]/(g(x)) let d = x+(g(x)), so that Z2[2]/(g(x)) = Z2(8). Express 8 and (82 + 1)-1 in the form a + b8 + co² + d8³, where a, b, c, d e Z2.

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