Find all polynomials $P(x)$ with real coefficients such that the polynomial $$Q(x) = (x + 1)P(x-1) -(x-1)P(x)$$is constant.
Source: New Zealand NZMOC Camp Selection Problems 2016 p5
Tags: algebra, polynomial
Find all polynomials $P(x)$ with real coefficients such that the polynomial $$Q(x) = (x + 1)P(x-1) -(x-1)P(x)$$is constant.