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Cute and easy polynomial problem

Source: 2022 Bulgarian Spring Math Competition, Problem 8.1

March 27, 2022
polynomialalgebrafactoring polynomials

Problem Statement

Let P=(x4−40x2+144)(x3−16x)P=(x^4-40x^2+144)(x^3-16x). a)a) Factor PP as a product of irreducible polynomials. b)b) We write down the values of P(10)P(10) and P(91)P(91). What is the greatest common divisor of the two numbers?
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