Question

Thực hiện phép chia

(x⁵+x³+x²+1):(x⁵+1)

Giúp mik với ạ:))

Answer 1

Ta có: \(\left(x^5+x^3+x^2+1\right):\left(x^5+1\right)\)

\(=\frac{x^3\left(x^2+1\right)+\left(x^2+1\right)}{\left(x+1\right)\left(x^4-x^3+x^2-x+1\right)}\)

\(=\frac{\left(x^2+1\right)\left(x^3+1\right)}{\left(x+1\right)\left(x^4-x^3+x^2-x+1\right)}\)

\(=\frac{\left(x^2+1\right)\left(x+1\right)\left(x^2-x+1\right)}{\left(x+1\right)\left(x^4-x^3+x^2-x+1\right)}\)

\(=\frac{x^4-x^3+x^2+x^2-x+1}{x^4-x^3+x^2-x+1}\)

\(=\frac{x^4-x^3+2x^2-x+1}{x^4-x^3+x^2-x+1}\)