In the product of the solution (1) (ax 2+bx+1) and (2x 2-3x+1).

The items containing x 3 are: (2b-3a) x 3,

Items containing x are: (b-3) x,

Because this product contains neither x 3 term nor x term,

So 2b-3a = 0, b-3 = 0,

So a = 2 and b = 3.

(2) Because A+B = 7 and AB = 1 1,

So (a-b) 2 = (a+b) 2-4ab.

=49-44

=5,

So (a-b) 4 = 25.

(3) Let this cubic polynomial about X be: AX 3+BX 2+CX+D.

Then because when x is equal to 0, 1 and-1, 2, the values of polynomials are-1, -2, 0 and 3 respectively.

So d =- 1

a+b+c+d= - 2

- a+b - c+d=0

8a+4b+2c+d=3

To solve this system of equations:

a= 1，b=0，c= - 2，d= - 1

So this polynomial about x is: x 3-2x- 1.

(4)(a-b+c-d)(c-a-d-b)=(c-b-d+a)(c-b-d-a)

= (C-B-d)^2-a^2

= c 2+b 2+d 2-2cd+2bd-a^2 BC.