construct/rlve polynomial integer roots
construct/rlve polynomial integer roots: a task in MathConstructOptimize-Envs-harbor (Harbor dataset). The degree-8 polynomial P(x) = (147456) x^0 + (18432) x^1 + (-40960) x^2 + (-512) x^3 + (3328) x^4 + (-72) x^5 + (-100) x^6 + (2) x^7 + (1) x^8 can be written as (x - a 1)(x - a 2)...(x - a 8)…
The task
The degree-8 polynomial P(x) = (147456)*x^0 + (18432)*x^1 + (-40960)*x^2 + (-512)*x^3 + (3328)*x^4 + (-72)*x^5 + (-100)*x^6 + (2)*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.