Question

x^7+1

Answer 1

\(x^7+1\)

\(=x^7-x^6+x^5-x^4+x^3-x^2+x+x^6-x^5+x^4-x^3+x^2-x+1\)

\(=\left(x^7-x^6+x^5-x^4+x^3-x^2+x\right)+\left(x^6-x^5+x^4-x^3+x^2-x+1\right)\)

\(=x\left(x^6-x^5+x^4-x^3+x^2-x+1\right)+\left(x^6-x^5+x^4-x^3+x^2-x+1\right)\)

\(=\left(x^6-x^5+x^4-x^3+x^2-x+1\right)\left(x+1\right)\)

Answer 2

x^7+1=(x+1)(x^6-x^5+x^4-x^3+x^2-x+1)