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)....

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.