\(P\left(x\right)=\left(x^{99}-99x^{98}\right)-\left(x^{98}-99x^{97}\right)+\left(x^{97}-99x^{96}\right)-...-\left(x^2-99x\right)+x-1\)
\(=\left(x-99\right)\left(x^{98}-x^{97}+x^{96}-...+x^2-x\right)+x-1\)
\(P\left(99\right)=\left(99-99\right)\left(99^{98}-99^{97}+99^{96}-...+99^2-99\right)+99-1=98\)
Ta có : x = 99
=> 100 = x + 1
Ta có : P(99) = x99 - (x + 1)x98 + (x + 1)x97 - (x + 1)x96 + ..... + (x + 1)x - 1
= x99 - x99 - x98 + x98 + x97 - x97 - x96 + .... + x2 + x - 1
= x - 1
= 99 - 1 = 98
