Question

phan tich da thuc thanh nhan tu

x¹⁰+x⁸+x⁶+x⁴+x²+1

Answer 1

\(x^{10}+x^8+x^6+x^4+x^2+1=x^8\left(x^2+1\right)+x^4\left(x^2+1\right)+\left(x^2+1\right)\)\(=\left(x^2+1\right)\left(x^8+x^4+1\right)=\left(x^2+1\right)\left(x^8-x^2+x^4+x^2+1\right)\)

\(=\left(x^2+1\right)[x^2\left(x-1\right)\left(x^3+1\right)\left(x^2+x+1\right)+\left(x^2+x+1\right)\left(x^2-x+1\right)]\)

\(=\left(x^2+1\right)\left(x^2+x+1\right)\left(x^6-x^5+x^3-x+1\right)\)

Answer 2

= \(x^8\left(x^2+1\right)+x^4\left(x^2+1\right)+\left(x^2+1\right)\)

\(=\left(x^2+1\right)\left(x^8+x^4+1\right)\)