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For which n is the polynomial reducible?

Source: Czech-Polish-Slovak 2005 Q3

April 27, 2013
algebrapolynomialmodular arithmeticquadraticsalgebra unsolved

Problem Statement

Find all integers n≥3n \ge 3 for which the polynomial W(x)=xn−3xn−1+2xn−2+6W(x) = x^n - 3x^{n-1} + 2x^{n-2} + 6 can be written as a product of two non-constant polynomials with integer coefficients.
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