f(x)=x^4+x^3+x^2+x+1
=(x-2+2)^4+(x-2+2)^3+(x-2+2)^2+(x-2+2)+1
=(x-2)^4+4(x-2)^3*2+6(x-2)^2*4+4(x-2)*8+16
+(x-2)^3+3(x-2)^2*2+3(x-2)*4+8
+(x-2)^2+2(x-2)*2+4
+(x-2)+2
+1
=...
=(x-2+2)^4+(x-2+2)^3+(x-2+2)^2+(x-2+2)+1
=(x-2)^4+4(x-2)^3*2+6(x-2)^2*4+4(x-2)*8+16
+(x-2)^3+3(x-2)^2*2+3(x-2)*4+8
+(x-2)^2+2(x-2)*2+4
+(x-2)+2
+1
=...