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## Homework Statement

Find all polynomials P(x), such that P(x² - 2x) = [P(x-2)]²

## Homework Equations

Polynomial equations

## The Attempt at a Solution

Let x = y+2, then

P(y²+2y) = P²(y)

I tried to analyse by derivating

P'(y²+2y)(2y+2) = 2P(y)P'(y)

P'(y²+2y)(y+1) = P'(y)P(y)

I am not sure if I derivated correctly, though

Yet, that's it. Any ideas?