3. Consider the ring R[x], and its ideal I = (x²). Then the quotient ring R[T]/I provides an abstract construction of the ring R[ε]. (a) Define a function : R[e] → R[x]/I by (a + b) = a+bx+ I Verify that is a ring homomorphism. (b) Consider a polynomial f(x) = a + bx+c₂x² + c3x³ + + Cnx" €R[x]. Show that f(x) + I = a + bx + I are equal as equivalence classes. (c) Using part (b), explain why the homomorphism from part (a) is surjective.

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