A = x^100 - 21x^99 - 21x^98 - 21x^97 -...-21x^2 - 21x +2010
A=x^100 - 22x^99 + x^99 -22x^98 + x^98 - ... - 22x +x +2010
A=x^99 (x-22) + x^98 (x-22) + x^97(x-22) + ... + x(x-22) + x +2010
A=(x-22) (x^99 + x^98 + x^97 + ... + x) + x + 2010
Thay x = 22 vào A, tao có:
A= (22-22) (22^99 + 22^98 + ... +22) + 22 + 2010
A = 0 (22^99 + 22^98 + ... +22) + 2032
A= 0 + 2032
A = 2032
x=22
=>x-1=21
thay 21=x-1 vào A ta được:
A=x100-(x-1)x99-(x-1)x98-(x-1)x97-...-(x-1)x2-(x-1)x+2010
=x100-x100+x99-x99+x98-x98+x97-...-x3+x2-x2+x+2012
=>A=x+2012
thay x=22 vào A=x+2012 ta được:
A=22+2012=2034
