Find the nonconstant polynomial \(P(x)\) such that

\(P(P(x)) = (x^2 + x + 1) P(x)\)

ant101 Dec 28, 2018

#1**0 **

I do not know but it looks interesting. I will be interested in the answer when it comes

Melody Dec 29, 2018

#2**+2 **

it's pretty clear P(x) can't be an odd degree so we'll try a 2nd degree polynomial

\(\text{Letting }P(x) = c_0 + c_1 x + c_2 x^2\\ \text{then grinding out the expansions of each side and equating like power of x coefficients}\\ \text{we get two solutions}\\ P(x) = 0\\ P(x) = x+x^2\)

Rom Dec 29, 2018