Are the following polynomials irreducible over Z2?

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The discussion focuses on the irreducibility of three specific polynomials over the field Z2: (a) x² + x + 1, (b) x² + 1, and (c) x² + x. It is established that Z2 contains only two elements, 0 and 1, which can be used to evaluate the polynomials for roots. The method of finding roots by solving p(x) = 0 is emphasized as a key technique for determining irreducibility.

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Are the following polynomials irreducible over Z2?

(a) x2 + x + 1
(b) x2 + 1
(c) x2 + x
 
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Have you had any thoughts on the problem?
 
Z2 only has 2 elements. Have you checked to see what each of them gives in these polynomials? Finding the roots of p(x)= 0 is often a good way to factor the polynomial p(x)!

And please write at least x^2 for x2, not "x2".
 
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