F4 Maths Dividing Polynomials4

Let :
x^4 + ax^2 + b = (x^2 + cx + d)(x^2 + x + 1) - 2x + 2
x^4 + ax^2 + 2x + b - 2 = (x^2 + cx + d)(x^2 + x + 1)
L.H.S. = x^4 + cx^3 + dx^2 + x^3 + cx^2 + dx + x^2 + cx + d
L.H.S. = x^4 + (c+1)x^3 + (d+c+1)x^2 + (d+c)x + d
Compare with coefficients of both sides :
c + 1 = 0 => c = -1
a = d+c+1 = d
d + c = 2 ==> d = 3 , and hence a = 3
d = b - 2 ==> 3 = b - 2 , b = 5