Question

Cho đa thức f(x)=x¹⁰-101x⁹+101x⁸-101x⁷+...+101x+2021. Tính f(100)

Answer 1

Ta có: x=100

\(\Leftrightarrow x+1=101\)

Ta có: \(f\left(x\right)=x^{10}-101x^9+101x^8-101x^7+...+101x+2021\)

\(=x^{10}-x^9\cdot\left(x+1\right)+x^8\left(x+1\right)-x^7\left(x+1\right)+...+x\left(x+1\right)+2021\)

\(=x^{10}-x^{10}-x^9+x^9+x^8-x^8-x^7+...+x^2+x+2021\)

\(=x+2021\)

\(=100+2021=2121\)