( 1)

Let x=- 1, and the equation becomes [(-1) 2+2 * (1)+2] 5 = A0.

So a0= 1.

X=0, the equation becomes 2 5 = A0+a1+A2+...+A10.

So a1+A2+…+A10 = 25-1= 32-1= 31.

(2)

According to the left and right derivatives, it is still equal!

After the left derivative = 5 * (x2+2x+2) 4 * (2x+2); After the right derivative = a1+2a2 (x+1)+…+9a9 (x+1) 8+10a10 (x+1) 9.

Let x= 1, then 5 * 24 * 2 = a1+2a2 …+9a9+10a 2 …+9a9+10a65438.