Question

Tìm dư A=x+x³+x²⁷+x²⁰¹⁷ chia cho x²⁺1

Answer 1

\(A=x+x^3+x^{27}+x^{2017}=\left(x^{2017}+x^3\right)+\left(x^{27}+x\right)\)

\(=x^3\left(x^{2014}+1\right)+x\left(x^{26}+1\right)=x^3\left(\left(x^2\right)^{1007}+1\right)+x\left(\left(x^2\right)^{13}+1\right)\)Ta có \(x^3\left(\left(x^2\right)^{1007}+1\right)⋮x^2+1\) và \(x\left(\left(x^2\right)^{13}+1\right)⋮x^2+1\)

\(\Rightarrow A=x^3\left(\left(x^2\right)^{1007}+1\right)+x\left(\left(x^2\right)^{13}+1\right)⋮x^2+1\)

Do đó số dư khi chia A cho \(x^2+1\) là 0