Question: Please give me a prompt response with a brief answer. I would be eternally grateful. This is my homework.Thanks! (5pts) True or false questions. There

Please give me a prompt response with a brief answer. I would be eternally grateful. This is my homework.Thanks!

(5pts) True or false questions. There are 5 statements in the following. Please answer whether the statement is true or not (you don't need to give any reasons). (1) If F is a field, then F[x] is also a field. (2) The units in R[x] are precisely the units in R. (3) 24 + 2r' is an irreducible polynomial in Za(x]. (4) Let 62 be the evaluation homomorphism at 2 in Zs(x]. Then, 63((r + 2x)(x* + 1)(al2 +2)) =0. (5) as + 2r + 1 is a zero divisor in Za[x]

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