x^3=a(x-1)^3+b(x-1)^2+c(x-1)+d =ax^3-3ax^2+3ax-a+bx^2-2bx+b+cx-c+d =ax^3+(b-3a)x^2+(3a+c)x+b+d-a-c a=1 b-3a=0 b=3 3a+c=0 c=-3 b+d-a-c=0 d=-5