x^7 + x^5 + 1
=x^7-x^6+x^5-x^3+x^2+x^6-x^5+x^4-x^2+x+x^5-x^4+x^3-x+1
=(x^2+x+1)(x^5-x^4+x^3-x+1)
+x^4 - 6x^3 + 12x^2 - 14x + 3
=x^4-2x^3+3x^2-4x^3-6x^2-12x+x^2-2x+3
=(x^2-4x+1)(x^2-2x+3)
x^7 + x^5 + 1
=(x^2+x+1)(x^5-x^4+x^3-x+1)
\(x^7+x^5+1\)
\(=\left(x^7-x\right)\left(x^5-x^2\right)+\left(x^2+x+1\right)\)
\(=x\left(x^3-1\right)\left(x^3+1\right)+x^2\left(x^3-1\right)+\left(x^2+x+1\right)\)
\(=\left(x^2+x+1\right)\left(x-1\right)\left(x^4+x\right)+x^2\left(x-1\right)\left(x^2+x+1\right)+\left(x^2+x+1\right)\)
\(=\left(x^2+x+1\right)\left[\left(x^5-x^4+x^2-x\right)+\left(x^3-x^2\right)+1\right]\)
\(=\left(x^2+x+1\right)\left(x^5-x^4+x^3-x+1\right)\)
cái dấu cộng thứ hai mik đang làm cho bạn khác bấm nhầm vào trong đây. Xin lỗi
x7 + x5 + 1
= x7 + x6 - x6 + 2x5 - x5 + x4 - x4 + x3 - x3 + x2 - x2 + 1
= x2 . ( x5 - x4 + x3 + 1 ) + x . ( x5 - x4 + x3 + 1 ) + ( x5 - x4 + x3 + 1 )
= ( x2 + x + 1 ) . ( x5 - x4 + x3 + 1 )
