construct/rlve polynomial integer roots
construct/rlve polynomial integer roots: a task in MathConstructOptimize-Envs-harbor (Harbor dataset). The degree-8 polynomial P(x) = (126000) x^1 + (74700) x^2 + (5860) x^3 + (-4163) x^4 + (-836) x^5 + (22) x^6 + (16) x^7 + (1) x^8 can be written as (x - a 1)(x - a 2)...(x - a 8) with integers a…
The task
The degree-8 polynomial P(x) = (126000)*x^1 + (74700)*x^2 + (5860)*x^3 + (-4163)*x^4 + (-836)*x^5 + (22)*x^6 + (16)*x^7 + (1)*x^8 can be written as (x - a_1)(x - a_2)...(x - a_8) with integers a_1, ..., a_8 (not necessarily distinct). Find such integers.