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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...

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Advance Math

Write f(x)=x^4+2x^3+2x+1 as a product of irreduciblepolynomials, 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 amongthe polynomial rings in that exercise, so that the factor ringD/?f(? x)??i becomes a field. Find the inverse of x+?f? (x)??i inthis field.

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