Name for this family of polynomials

Question

I have a multivariable polynomial with powers of variables equal to $1$ or $0$, e.g. $$ 1=a+b+c-2ab-2bc-2ac+3abc. $$ What is the name for this type of polynomial?

Answer 1

I don't think this has a name. Notice that the RHS is

$$\left.\dfrac d{dx}(ax-1)(bx-1)(cx-1)\right|_{x=1},$$ which generalizes to more factors.