construct/rlve polynomial integer roots
construct/rlve polynomial integer roots: a task in MathConstructOptimize-Envs-harbor (Harbor dataset). The degree-8 polynomial P(x) = (-1152) x^0 + (-3024) x^1 + (-2356) x^2 + (-96) x^3 + (519) x^4 + (102) x^5 + (-36) x^6 + (-6) x^7 + (1) x^8 can be written as (x - a 1)(x - a 2)...(x - a 8) with…
The task
The degree-8 polynomial P(x) = (-1152)*x^0 + (-3024)*x^1 + (-2356)*x^2 + (-96)*x^3 + (519)*x^4 + (102)*x^5 + (-36)*x^6 + (-6)*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.