My working for a):
a(x-1)<sup>2</sup> + b(x-1) + c = x<sup>2</sup>
.'. ax<sup>2</sup> - 2ax + a +bx - b +c = x<sup>2</sup>
.'. ax<sup>2</sup> - (2a-b)x + (a-b+c) = x<sup>2</sup>
Equating coefficients:
a=1
2a - b = 0 --> b=2
a - b + c = 0 --> c=1
.'. a=1, b=2, c=1