  Let $X$ be a three dimensional real Banach space. Ben\'itez and Otero \cite
{BeO} showed that if the unit ball of $X$ is is an intersection of two
ellipsoids, then every 2-polynomial defined in a linear subspace of $X$ can be
extended to $X$ preserving the norm. In this article, we extend this result to
any finite dimensional Banach space.
