Question

Cho đa thức:\(F\left(x\right)=x^{10}-101x^9+101x^8-101x^7+....-101x+101\\ \)

Tính \(F\left(100\right)\)

Answer 1

Ta có: 

\(F\left(100\right)=100^{10}-101.100^9+101.100^8-101.100^7+...-101.100+101\)

       \(=100-\left(100+1\right).100^9+\left(100+1\right).100^8-\left(100+1\right).100^7+...-\left(100+1\right).100+101\)

 \(=100^{10}-100^{10}-100^9+100^9+100^8-100^8-100^7+...-100^2-100+101\)

\(=1\)

Answer 2

Ta có:\(101=100+1=x+1\)

\(\Rightarrow F\left(100\right)=x^{10}-\left(x+1\right)x^9+\left(x+1\right)x^8-...-\left(x+1\right)x+x+1\)

\(=x^{10}-x^{10}-x^9+x^9+x^8-...-x^2-x+x+1=1\)