This question summarizes a few simple facts about polynomials. Recall that a polynomial $p$ can be written in the form $$p(x) = \sum_{i=0}^n \alpha_i x^i$$ where we assume that $\alpha_n\neq 0$. The degree of a polynomial is the largest exponent present, and so the degree of $p$ is $n$. Fill in the blanks in the following questions:

The degree of $p'(x)$ is .

The degree of $\int p(x) \hbox{d}x$ is .

The degree of $p^2(x)$ (i.e., the square of $p$) is .

The $(n+1)$-th derivative of $p$ is .