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2 2 Let $g(x, y, z)$ be a polynomial in the three variables $x, y, z$ that take values in $mathbb{N}$ . Prove that $g(x, y, z) = mathcal{O}(x^k y^l z^m)$ for some $k, l, m in mathbb{N}$ I am not sure how to approach the big $O$ method for multiple variables, the following post did not help me that much further Formal definition of big-O when multiple variables are involved?. So far we have only dealt with single-variable polynomials. Also, am I right in assuming that what is meant here is that the maximal degrees of $x$ , $y$ and $z$ in the polynomial are the numbers $k, l$ and $m$ ? asymptotics computational-complexity share | cite | improve this question