Please prove the following with clear steps and/or related theorem.Problem 3.(i) Prove or disprove: if R is a commutative ring and P and Q are polyno-mials in R[a], then P = Q if and only if P(a) = Q(a) for all a e R.(ii) Prove or disprove: if R is a commutative ring and P E R[x] is a polynomial whosecoefficients are zero divisors in R, then P is a zero divisor in R[x].(iii) (Bonus) Prove or disprove: if R is a commutative ring and P is a zero divisor in R[x],then every coefficient in P is a zero divisor in R.

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Answered: Problem 3. (i) Prove or disprove: if R…

Problem 3. (i) Prove or disprove: if R is a commutative ring and P and Q are polyno- mials in R[x], then P = Q if and only if P(a) = Q(a) for all a e R. %3D

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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