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Primitive polynomials and irreducible polynomials

1) How do I show x+1 is primitive?

2) How do I prove x^4+x^3+1 is an irreducible polynomial of degree 4 over Z mod?

Solution Preview

x+1 is primitive because the greatest common divisor of the coefficients 1 and 1 is 1.

2) x^4+x^3+1 can be written as x^4+x^3+0x^2+0x+1
Since the coefficients ...