Polynomials/R/Group homomorphism/Exercise

a) For what real polynomials ${}P\in \mathbb {R} [X]$ is the corresponding polynomial mapping

$(\mathbb {R} ,0,+)\longrightarrow (\mathbb {R} ,0,+),x\longmapsto P(x),$

a group homomorphism?

b) For what real polynomials ${}Q\in \mathbb {R} [X]$ is the polynomial mapping

$(\mathbb {R} ^{\times },1,\cdot )\longrightarrow (\mathbb {R} ^{\times },1,\cdot ),x\longmapsto Q(x),$

well-defined and a group homomorphism?

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