# A polynomial product

Algebra Level 4

$$f_1 (x), f_2(x), f_3(x), f_4(x)$$ and $$f_5 (x)$$ are 5 non-constant polynomials with integer coefficients such that

$f_1 (x) \times f_2(x) \times f_3(x) \times f_4(x) \times f_5(x) = x^8 + 3x^4 - 4.$

What is the value of $\lvert f_1(1) \rvert + \lvert f_2(1) \rvert + \lvert f_3(1) \rvert + \lvert f_4(1) \rvert + \lvert f_5(1) \rvert ?$

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