Quaint quintic

Algebra Level 3

The polynomial expression in two variables

f(x,y)=x5+3y23x2+y5 f(x,y) = x^5 + 3y^2 - 3x^2+y^5

can be factorized into the product of two non-constant polynomials with integer coefficients, namely

f(x,y)=g(x,y)×h(x,y). f(x,y) = g(x,y) \times h(x,y).

Evaluate g(2,2)+h(2,2).|g(2,2)|+|h(2,2)|.

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