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  3. f: r[x] to r is the map defined as f(p(x))=p(2) fo

f: R[x] to R is the map defined as f(p(x))=p(2) for any polynomial p(x) in R[x]. show...

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Advance Math

f:R[x] to R is the map defined as f(p(x))=p(2) for any polynomialp(x) in R[x]. show that f is
1) a homomorphism
2) Ker(f)=(x-2)R[x]
3) prove that R[x]/Ker(f) is an isomorphism with R.
(R in this case is the Reals soR[x]=a0+a1x+a1x^2...anx^n)

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