(a) Check whether R = Q[x]/<x3+18x2+3x+6> is a field or not. If R is a field, find its characteristic. If R is not a field, obtain its quotient field.
(b) Prove the following stateinent using the principle of mathematical induction :If p (x) ao + a1x + anxn belongs to. R [x] and a belongs to R, then p (x) can be written as bo + b1(x — a) +... +bn (x — a)n, bi belongs to R for all i = 0,1,2,...n.
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