Question

ptdttnt

x^20+x+1

Answer 1

\(x^{20}+x+1=\left(x^{20}-x^2\right)+\left(x^2+x+1\right)\)

\(=x^2\left(x^{18}-1\right)+x^2+x+1\)

\(=x^2\left(x^6-1\right)\left(x^{12}+x^6+1\right)+x^2+x+1\)

\(=\left(x^{14}+x^8+x^2\right)\left(x^6-1\right)+x^2+x+1\)

\(=\left(x^{14}+x^8+x^2\right)\left(x^3+1\right)\left(x-1\right)\left(x^2+x+1\right)+x^2+x+1\)

\(=\left(x^{18}-x^{17}+x^{15}-x^{14}+x^{12}-x^{11}+x^9-x^8+x^6-x^5+x^3-x^2+1\right)\left(x^2+x+1\right)\)