Let p: Q[x] → M2(R) be defined by p(ao + a1 + a2x² + ...+ anx") = ( ) ao (1) Write down o(2 +x – x³), y(2a² + 7æ³), p(x² – x). (2) Show that y is a ring homomorphism. (3) Find a polynomial p(x) such that ker o = (p(x)). (4) Find a subring of M2(R) isomorphic to the quotient Q[x]/{p(x)).

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