Quaint quintic

Algebra Level 3

The polynomial expression in two variables

\[ f(x,y) = x^5 + 3y^2 - 3x^2+y^5 \]

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

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

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

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