Question

X^16-1

Answer 1

\(x^{16}-1=\left(x^8-1\right)\left(x^8+1\right)\)

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

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

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

Answer 2

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