I just started on this topic, but when i come the polynomial. I don't have any idea where to start.

Consider the time series $\displaystyle {Y_t}$ and let $\displaystyle D$ be first difference operator $\displaystyle Dy_t = y_t - y_{t-1}$

1.If $\displaystyle y_t$ is a polynomial in $\displaystyle t$ of order $\displaystyle k$ then prove that $\displaystyle Dy$ is polynomial of order $\displaystyle k-1$.

2. Suppose $\displaystyle Y_t = p(t) + U_t$ where $\displaystyle p(t)$ is a polynomial of degree $\displaystyle k$ and $\displaystyle U_t$ is a stationary noise process. Show that $\displaystyle D^kY$ is stationary process.

Please help me, thank you.