 Homogeneous polynomial

A polynomial is homogeneous of degree $n$ when scaling all variables by $\lambda$ scales its value by ${\lambda }^n$.

A **homogeneous polynomial** is a polynomial whose terms all have the same total degree. In more formal terms, a polynomial \( P(x_1, x_2, \ldots, x_n) \) is called homogeneous of degree \( d \) if every term in the polynomial is of degree \( d \).