Here I prove that $P(x,y)=\frac{(x+y)^2+3x+y}{2}$ works. It is clearly second degree. This is a good way to show that $|\mathbb{Q}_{\geq0}|\leq|\mathbb{Z}_{\geq0}|$ and to establish that the integers and rationals are one-to-one. Additionally, we can show that for $k$ variables, there is a degree $k$ equation that satisfies the question, namely $P(a_1, a_2, \ldots a_k)=\sum_{n=1}^{k}{{a_1+a_2+a_3\ldots+a_n+(n-1)}\choose{n}}$. We can show this through the same process as in the other post.