Funky Functional Equation Part II

Algebra Level 5

Find the absolute value of the product of two possible values for \(f(10)\) given that

\(f(xf(x)+f(y))=y+f(x)^2\)

Where \(x, y \in \mathbb{R}\) and \(f(x)\) is a polynomial function.


Note: This question has been edited several times, and is now correct.

See Part I if you enjoyed this problem! :D

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