ILL 1979 Problem 10

Find all polynomials $f(x)$ with real coefficients for which $f(x)f(2x^2) = f(2x^3 + x).$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.