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P(x) = x^5 - 3x^4 + 6x^3 - 3x^2 + 9x - 6

Source: Polish MO Finals 1963 p5

August 30, 2024
algebrapolynomial

Problem Statement

Prove that a fifth-degree polynomial P(x)=x5−3x4+6x3−3x2+9x−6 P(x) = x^5 - 3x^4 + 6x^3 - 3x^2 + 9x - 6 is not the product of two lower-degree polynomials with integer coefficients.
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