1/ \(x^6+x^4-x^2-1=\left(x^6+x^4\right)-\left(x^2-1\right)\)
=\(x^4\left(x^2+1\right)-\left(x^2+1\right)\)
=\(\left(x^2+1\right)\left(x^4-1\right)\)
=\(\left(x^2+1\right)\left(x^2-1\right)\left(x^2+1\right)\)
1) x6 + x4 - x2 - 1 = x4 (x2 + 1 ) - ( x2 + 1 ) = (x4 - 1) (x2 + 1)
= (x2 + 1 ) (x2 - 1) (x2 + 1 ) =(x2 + 1 )2 (x + 1)(x- 1)
2) x7 + x5 + x4 + x3 + x2 + 1 = x4 ( x3+ x2 + 1) + ( x3+ x2 + 1)
= (x4 + 1)( x3+ x2 + 1)
3) x2y + xy2 + x2z + xz2 + y2z + yz2 + 2xyz
= xy(x + y) + xz(x + z) + yz( y+ z) + xyz +xyz
= xy(x + y +z ) + xz(x + y + z) + yz( y+ z )
= x ( x + y + z ) (y + z) + yz ( y +z )
=( y + z) [ x(x + y + z) + yz]
=(y + z ) (x2 + xy + xz + yz)
( Tớ hơi làm tắt nên có chỗ nào không hiểu thì cậu nói cho tớ nhé!
)
phần 2 tớ làm sai, sửa lại nhé!
x7 + x5 + x4 + x3 + x2 + 1 = ( x7 + x5 + x3 ) + (x4 + x2 + 1 )
= x3 ( x4 + x2 + 1) + (x4 + x2 + 1)
= (x3 + 1)( x4 + x2 + 1)
= (x + 1 ) (x2 + x +1) (x4 + x2 + 1)
