  We prove that the local $\mathbb{A}^1$-degree of a polynomial function at an
isolated zero with finite separable residue field is given by the trace of the
local $\mathbb{A}^1$-degree over the residue field. This fact was originally
suggested by Morel's work on motivic transfers and by Kass and Wickelgren's
work on the Scheja-Storch bilinear form. As a corollary, we generalize a result
of Kass and Wickelgren's relating the Scheja-Storch form and the local
$\mathbb{A}^1$-degree.
