\(x^{16}+x^8+1\)
\(=\left(x^8\right)^2+2.x^8.\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2+\dfrac{3}{4}\)
\(=\left(x^8+\dfrac{1}{2}\right)^2+\dfrac{3}{4}\)
\(x^{16}+x^8+1\)
\(=\left(x^{16}+2x^8+1\right)-x^8\)
\(=\left(x^8+1\right)^2-\left(x^4\right)^2\)
\(=\left(x^8+1-x^4\right)\left(x^8+1+x^4\right)\)
\(=\left(x^8-x^4+1\right)\left[\left(x^8+2x^4+1\right)-x^4\right]\)
\(=\left(x^8-x^4+1\right)\left[\left(x^4+1\right)^2-\left(x^2\right)^2\right]\)
\(=\left(x^8-x^4+1\right)\left[\left(x^4-x^2+1\right)\left(x^4+x^2+1\right)\right]\)
\(=\left(x^8-x^4+1\right)\left\{\left(x^4-x^2+1\right)\left[\left(x^4+2x^2+1\right)-x^2\right]\right\}\)
\(=\left(x^8-x^4+1\right)\left\{\left(x^4-x^2+1\right)\left[\left(x^2+1\right)^2-x^2\right]\right\}\)
\(=\left(x^8-x^4+1\right)\left(x^4-x^2+1\right)\left(x^2-x+1\right)\left(x^2+x+1\right)\)
Học tốt !
