construct/rlve polynomial integer roots
construct/rlve polynomial integer roots: a task in MathConstructOptimize-Envs-harbor (Harbor dataset). The degree-8 polynomial P(x) = (-288) x^1 + (444) x^2 + (133) x^3 + (-455) x^4 + (166) x^5 + (10) x^6 + (-11) x^7 + (1) x^8 can be written as (x - a 1)(x - a 2)...(x - a 8) with integers a 1…
The task
The degree-8 polynomial P(x) = (-288)*x^1 + (444)*x^2 + (133)*x^3 + (-455)*x^4 + (166)*x^5 + (10)*x^6 + (-11)*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.