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problem 2 In the polynomial ring Z[x], let I = {a0 + a1x + ... +...

problem 2 In the polynomial ring Z[x], let I = {a0 + a1x + ... + anx^n: ai in Z[x],a0 = 5n}, that is, the set of all polynomials where the constant coefficient is a multiple of 5. You can assume that I is an ideal of Z[x]. a. What is the simplest form of an element in the quotient ring z[x] / I? b. Explicitly give the elements in Z[x] / I. c. Prove that I is not a principal ideal (that is, I does not equal <f(x)> for any polynomial f(x) in Z[x])

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