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In: Advanced Math

Write f(x)=x^4+2x^3+2x+1 as a product of irreducible polynomials, considered as a polynomial in Z3[x], Z5[x], and...

Write f(x)=x^4+2x^3+2x+1 as a product of irreducible polynomials, considered as a polynomial in Z3[x], Z5[x], and Z7[x], respectively.

1. 2. Let f(x) be as in the previous exercise. Choose D among the polynomial rings in that exercise, so that the factor ring D/〈f(├ x)〉┤i becomes a field. Find the inverse of x+〈f├ (x)〉┤i in this field.

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