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(X^2-12X +11)^4+23 not product of 3 integer polynomials

Source: 2015 Saudi Arabia Pre-TST 3.2

September 12, 2020
polynomialInteger Polynomialalgebra

Problem Statement

Prove that the polynomial P(X)=(X2āˆ’12X+11)4+23P(X) = (X^2-12X +11)^4+23 can not be written as the product of three non-constant polynomials with integer coefficients.
(Le Anh Vinh)
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