Hi guys, I need your help again! I'm going through a proof in a textbook, and I can't prove the following two results

1) Let $\displaystyle \beta_1, \beta_2, \ldots, \beta_m$ be the roots of an equation $\displaystyle dx^m+d_1x^{m-1} + \ldots + d_m = 0$. Then, any symmetrical integral polynomial in $\displaystyle d\beta_1, d\beta_2, \ldots, d\beta_m$ is an integral polynomial in $\displaystyle d_1, d_2, \ldots, d_m$ and therefore an integer.

2) Any symmetrical integral polynomial in $\displaystyle d\alpha_1, \ldots, d\alpha_n$ is a symmetrical integral polynomial in $\displaystyle d\alpha_1, \ldots, d\alpha_n, 0, 0, \ldots, 0$.

Thanks.