Ta có : x8 + x + 1
= x8 - x5 + x5 - x2 + x2 + x + 1
= x5 (x3 - 1 ) + x2 ( x3 - 1 ) + x2 + x + 1
= x5 (x - 1)( x2 + x + 1 ) + x^2 ( x - 1 )( x2 + x + 1 ) + x2 + x + 1
= ( x6 - x5 )( x2 + x + 1 ) + ( x3 - x2 )(x2 + x + 1 ) + (x2 + x + 1)
= (x2 + x + 1) ( x6 - x5 + x3 - x2 + 1)
\(x^8+x+1\)
\(=\left(x^8-x^5\right)+\left(x^5-x^2\right)+\left(x^2+x+1\right)\)
\(=x^5\left(x^3-1\right)+x^2\left(x^3-1\right)+\left(x^2+x+1\right)\)
\(=x^5\left(x-1\right)\left(x^2+x+1\right)+x^2\left(x-1\right)\left(x^2+x+1\right)+\left(x^2+x+1\right)\)
\(=\left(x^2+x+1\right)\left(x^6-x^5+x^3-x^2+1\right)\)
x8 + x + 1
= x8 - x5 + x5 -x2 + x2 + x + 1
= ( x8 - x5 ) + ( x5 - x2 ) + ( x2 + x + 1 )
= x5 ( 9 x - 1 ) ( x2 + x + 1 ) + x2 ( x - 1 ) ( x2 + x + 1 ) + ( x2 + x + 1 )
=(( x5 + x2 ) ( x - 1 ) +1 ) ( x2 + x + 1 )
x8+x+1=x8+x7+x6+x5+x4+x3+x2+x+1-x7-x6-x5-x4-x3-x2
=(x6-x5+x3-x2+1)(x2+x+1)
Còn phân tích được nữa hay không thì mình không nhớ, mình chỉ nhớ đến đó thôi ^ ^ Thông cảm nha
\(x^8+x+1\)
\(=x^8+x^7+x^6-x^7-x^6-x^5+x^5+x^4+x^3-x^4-x^3-x^2+x^2+x+1\)
\(=x^6\left(x^2+x+1\right)-x^5\left(x^2+x+1\right)+x^3\left(x^2+x+1\right)-x^2\left(x^2+x+1\right)+x^2+x+1\)
\(=\left(x^2+x+1\right)\left(x^6-x^5+x^3-x^2+1\right)\)
