Every non-negative multivariate polynomial has degree even?

Question

Is it true that every non-negative multivariate polynomial with $n$ variable on $\mathbb R$ has even degree?

By degree of polynomial I mean greatest sum of powers of variables for each monomial.

Answer 1

Indeed, suppose any variable $y$ appears to a greatest power $m$ which is odd (holding all other variables constant such that the coefficient of $y^m$ is nonzero). Then by sending $y$ to $-\infty$, we can make the expression become as negative as we wish.