An Odd Cubic from Two Limits

Difficulty: Medium · Topics: Calculus, Limits, Polynomials

Ikki limitdan toq kub ko‘phad

d[P(x)]=3, for all a∈mathbbR P(a)+P(-a)=0, and

lim x→ 1(P(x))/(x-1)=k∈mathbbR, lim x→∞fracP(x)x^3=3.

Find k.