Alright i am working on homework and got stuck on a problem, looked it up online and im unsure of how they did a particular point.

Problem:

A(x-2)(x2+2) + B(x+2)(x2+2) + (Cx+D)(x2-4) = x2

(A+B+C)x3 + (-2A+2B+D)x2 + (2A+2B-4C)x + (-4A+4B-4D) = x2

A+B+C=0

**(1)** Use 4.

**(2)** +

**(4)**
-2A+2B+D=1

**(2)** >> -3A+3B=1

**(5)**
2A+2B-4C=0

**(3)** Use 4.

**(1)** +

**(3)**
-4A+4B-4D=0

**(4) >> **6A+6B = 0

**(6)**

I know the work is correct, however i am unsure of how you get

(A+B+C)x3 + (-2A+2B+D)x2 + (2A+2B-4C)x + (-4A+4B-4D)

**And how you decide the numbers in **
A+B+C=0

**(1)** Use 4.

**(2)** +

**(4)**
-2A+2B+D=1

**(2)** >> -3A+3B=1

**(5)**
2A+2B-4C=0

**(3)** Use 4.

**(1)** +

**(3)**
-4A+4B-4D=0

**(4) >> **6A+6B = 0

**(6)**

For instance, how do you know A+B+C=0? why not A+B+C=1?