From the looks of it, it is just smart substitution. Basically, you want to pick values for "x" in such a way that one of the variables disappear. Do this enough times and you can get a solvable set of equations.
So for (2)
Pick x = 1 (doing this removes the a variable)
We get:
4b + c = 1
Now pick x = -1 (doing this removes the b variable)
We get:
4a + c = 1
Now there is no way to remove the c variable so let's just pick x = 0.
We get:
a + b + c = 0
Now we have 3 set of equations and 3 variables.
Solve this by using Gauss-Jordan elimination or whatever other technique you know (Or just use an online matrix calculator).
You should get:
a = 1/2
b = 1/2
c = -1
