Polynomials with integer coefficients

Algebra Level 4

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

f(x)×g(x)=x5x2x1. f(x) \times g(x) = x^5 - x^2 - x - 1.

What is the value of f(3)+g(3) \lvert f(3) + g(3) \rvert ?

Details and assumptions

You may use the fact that f(3)×g(3)=230 f(3) \times g(3) = 230 .


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