For an even weight function prove that the orthogonal polynomial is even or odd function depending on the grade.

Question

Let $w(x)$ be an even weight function and [a,b] is a symmetric region with respect to $0$. Prove that the orthogonal polynomial satisfies $p_{n}(-x)=(-1)^{n}p_{n}(x)$ for $n=0,1,2..$

It says that an orthogonal polynomial with respect to an even weight function, is even or odd function depending on its grade.