Advanced factorization is a gateway to algebraic number theory, which mathematicians study in order to solve famous conjectures like Fermat's Last Theorem.

Given that \(f(x) \) and \(g(x) \) are two non-constant polynomials with integer coefficients such that

\[ f(x) \times g(x) = x^6-6x^5+4x^4-12x^3-8,\]

evaluate \(\lvert f(2)+g(2) \rvert.\)

**Details and assumptions**

You may use the fact that \( f(2) \times g(2) = -168 \).

Let \( f(x) = x^2 - 1 \). How many distinct real roots are there to \( f ( f( f(x))) = 0 \)?

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