Let Z2[x] be the ring of all polynomials with coefficients

Chapter 14, Problem 51E

(choose chapter or problem)

Let \(Z_2[x]\) be the ring of all polynomials with coefficients in \(Z_2\) (that is, coefficients are 0 or 1, and addition and multiplication of coefficients are done modulo 2). Show that \(Z_{2}[x] /\left\langle x^{2}+x+1\right\rangle\) is a field.

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