construct/rlve polynomial integer roots

construct/rlve polynomial integer roots: a task in MathConstructOptimize-Envs-harbor (Harbor dataset). The degree-5 polynomial P(x) = (40) x^1 + (78) x^2 + (49) x^3 + (12) x^4 + (1) x^5 can be written as (x - a 1)(x - a 2)...(x - a 5) with integers a 1, ..., a 5 (not necessarily distinct). Find…