Problem 4. Consider the polynomial ring C[t], where C is the field of complex numbers. (4-1) Show that (t -a) is a maximal ideal of C[t] for any a e C. (4-2) Let f (t) = t³ (t – 1)² e C[t], and let I be the ideal of C[t] generated by f (t). Find every prime ideal of C[t]/I.

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