MathNet 2017-part-03 — 176 problems (EN–VI) Question 58

Let $d$ be a nonnegative integer. Determine all functions $f : \mathbb{R}^2 \to \mathbb{R}$ such that, for any real constants $A$, $B$, $C$ and $D$, $f(At+B, Ct+D)$ is a polynomial in $t$ of degree at most $d$.