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Answer on Abstract Algebra Question for Annemarie

Question #5108
Let Z be the ring of integers. Consider the function
f : Z[x] → Z
defined by f(g(x)) = g(0). for example, f(x2 + 1) = 1.
(a) Show that f is a ring homomorpism.
(b) What is the ker(f)?
Expert's answer
1) we must show that f is save multiplication and addition
let h(x)=

f is ring homomorphism
2) Ker(f) all that polynoms such that g(0)=0 so it
have g(x)=x*h(x), where h - polynom from Z[x]

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