Let $$(x + 1)(x^2 + 2)(x^2 + 3)(x^2 + 4)(x^2 + 5) = \sum\_{k=0}^{9} (A\_k \cdot x^k)$$

Compute:

1. $$\displaystyle \sum\_{k=0}^{9} A\_k$$
2. $$\displaystyle \sum\_{k=0}^{4} A\_{2k}$$

I tried to figure out from Viete's Sums how to rewrite this but I can't find the coefficients for all powers of $x$. All I know is $A\_9 = 1, A\_0 = 1\cdot 2 \cdot 3 \cdot 4 \cdot 5$.