\(x^8+x+1\)
=\(x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1-x^7-x^6-x^5-x^4-x^3-x^2\)
\(x^6\left(x^2+x+1\right)+x^3\left(x^2+x+1\right)+x^2+x+1-x^5\left(x^2+x+1\right)-x^2\left(x^2+x+1\right)\)<=> \(\left(x^2+x+1\right)\left(x^6+x^3+1-x^5-x^2\right)\)
Cách 2: \(x^8+x+1\) = \(\left(x^8-x^2\right)+\left(x^2+x+1\right)\)
= \(x^2\left(x^6-1\right)+\left(x^2+x+1\right)\)
= \(\left(x^5+x^2\right)\left(x-1\right)\left(x^2+x+1\right)+\left(x^2+x+1\right)\)
= \(\left(x^2+x+1\right)\left(x^6-x^5+x^3-x^2+1\right)\)
Cách 2: x8+x+1x8+x+1 = (x8−x2)+(x2+x+1)(x8−x2)+(x2+x+1)
= x2(x6−1)+(x2+x+1)x2(x6−1)+(x2+x+1)
= (x5+x2)(x−1)(x2+x+1)+(x2+x+1)(x5+x2)(x−1)(x2+x+1)+(x2+x+1)
= (x2+x+1)(x6−x5+x3−x2+1)
x8+x+1
=x8+x7+x6-x7-x6-x5+x5+x4+x3-x4-x3-x2+x2+x+1
=x6(x2+x+1)-x5(x2+x+1)+x3(x2+x+1)-x2(x2+x+1)+(x2+x+1)
=(x2+x+1)(x6-x5+x3-x2+1)
