A= x^3(x-17) + 17x(x-1) +20
=16^3.(-1) +17.16.15+20 = (16+1)(16-1).16 -16^3+20
= (16^2-1).16 -16^3+20 = 16^3-16+16^3+20=4
B= x^4(x-15) + 16x^2(x-1) + 13x . (-x+1)
= -14^4 +16.14^2.13 + 13.14.(-13)= -14^4 +(15+1).14^2.13 -13^2.14
= -14^4 +15.14^2.13 + 14^2.13 - 13^2.14= -14^4 +(14+1).14^2.(14-1) -13^2.14
= -14^4 +(14^2-1).14^2 +13.14 = -14^4 +14^4 -14^2 +13.14= 14(13-14) = -14
\(A=x^4-17x^3+17x^2-17x+20\)
\(=x^4-\left(x+1\right)x^3+\left(x+1\right)x^2-\left(x+1\right)x+x+4\)
\(=x^4-x^4-x^3+x^3+x^2-x^2-x+x+4\)
\(=4\)
A = x4 - 17x3 + 17x2 - 17x + 20
x = 16 => 17 = x + 1
Thế vào A ta được
A = x4 - ( x + 1 )x3 + ( x + 1 )x2 - ( x + 1 )x + 20
= x4 - x4 - x3 + x3 + x2 - x2 - x + 20
= -x + 20
= -16 + 20 = 4
B = x5 - 15x4 + 16x3 - 29x2 + 23x
x = 14
=> 15 = x + 1
16 = x + 2
29 = 2x + 1
13 = x - 1
Thế vào B ta được :
B = x5 - ( x + 1 )x4 + ( x + 2 )x3 - ( 2x + 1 )x2 + ( x - 1 )x
= x5 - x5 - x4 + x4 + 2x3 - 2x3 - x2 + x2 - x
= -x
= -14
