AHSME 1983 Problem 6

When $x^5, x+\frac{1}{x}$ and $1+\frac{2}{x} + \frac{3}{x^2}$ are multiplied, the product is a polynomial of degree. $\textbf{(A)}\ 2 \textbf{(B)}\ 3 \textbf{(C)}\ 6 \textbf{(D)}\ 7 \textbf{(E)}\ 8$