F2 maths--Identity

1.) If x^2-4X+3=A(x-h)^2+k, Find A,h and k
lhs=x^2-4x+3
rhs=a(x-h)^2+k
=a(x^2-2xh+h^2)+k
=ax^2-2xha+ah^2+k
a=1
-4x=-2xh
h=2
h^2+k=3
4+k=3
k=-1

2.) If 3x^2+6x=A(x-h)^2+k, find A, h and k
lhs=3x^2+6x
rhs=a(x-h)^2+k
=a(x^2-2xh+h^2)+k
=ax^2-2axh+h^2+k
a=3
-2axh=6x
-2ah=6
ah=-3
3h=-3
h=-1
h^2+k =0
1+k=0
k=-1

3.) If -2x^2-6=Ax(x-3)+B(x-3)(x-1)+Cx(x-1), find A,B and C
lhs=-2x^2-6
rhs=ax(x-3)+b(x-3)(x-1)+cx(x-1)
=ax^2-3ax+b(x^2-4x+3)+cx^2-cx
=ax^2-3ax+bx^2-4xb+3b+cx^2-cx
=x^2(a+b+c)-x(3a+4b+c)+3b

we know that -x(3a+4b+c)=0*x
so 3a+4b+c=0...............................(1)
a+b+c=-2......................................(2)
3b=-6
b=-2
put b into list 1&2
3a+4(-2)+c=0
3a+c=8 ......(3)
a-2+c=0
a+c=2.........(4)
to list 3 min. list 4
2a=6
a=3
so 3+c=2
c=-1