1) let f(x) be a polynomial with integer coefficients satisfying f(2021) = 2020. assume that f(x) can be factored into five polynomials with integer coefficients: f(x) = g1(x)g2(x)g3(x)g4(x)g5(x). prove that the sum of the coefficients of at least one factor g(x) is odd.
1) let f(x) be a polynomial with integer coefficients satisfying f(2021) = 2020. assume that f(x) can be factored into five polynomials with integer coefficients: f(x) = g1(x)g2(x)g3(x)g4(x)g5(x). prove that the sum of the coefficients of at least one factor g(x) is odd.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.4: Complex And Rational Zeros Of Polynomials
Problem 37E
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1) let f(x) be a polynomial with integer coefficients satisfying f(2021) = 2020. assume that f(x) can be factored into five polynomials with integer coefficients: f(x) = g1(x)g2(x)g3(x)g4(x)g5(x). prove that the sum of the coefficients of at least one factor g(x) is odd.
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