In Z[x], let I = { f(x) E Z[x]: f(0) is an even integer). 1) Prove that I is an ideal of Z[x]. 2) What is the elements of Z[x]/ 1?

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Q: let I = ff) be a non-zero idea] of F[*].

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A: We are given : f(x)=x3+x2+x+0⇒f(x)=x3+x2+xand g(x)=x+[1]⇒g(x)=x+1Now, Dividing f(x) by  g(x), we…

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Q: Prove that the inner derivations ad x, x∈g are an ideal on Der(g)

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.