Algebra
# Advanced Factorization

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 $f ( f( f(x))) = 0$?