Are these two forms of factoring a polynomial the same?

Question

I was reading about polynomial factorization and there was something that was bothering me. If $P(x)$ is a polynomial (let’s say of degree $n \in \Bbb{N}$) with roots $x_1$, $x_2$, $\dots$, $x_n$, then we can write it as \begin{align*} P(x) = \prod_{i=1}^n(x-x_i). \end{align*} But can I also write \begin{align*} P(x) = \prod_{i=1}^n(x_i - x) \,\,\,\, ? \end{align*} If yes, what allows me to do this? Because in my mind I see different polynomials when $n$ is odd...