\(x^5+x^4+1\)

\(=x^5-x^3-x^2-x^4+x^2+x+x^3-x-1\)

\(=x^2\left(x^2-x-1\right)-x\left(x^3-x-1\right)+\left(x^3-x-1\right)\)

\(=\left(x^2-x+1\right)\left(x^3-x-1\right)\)

\(x^5+x^4+1=x^5+x^4+x^3-x^3+1=x^3\left(x^2+x+1\right)-\left(x^3-1\right)=x^3\left(x^2+x+1\right)-\left(x-1\right)\left(x^2+x+1\right)=\left(x^3-x+1\right)\left(x^2+x+1\right)\)

x^10 + x^5 + 1
= x^10 + x^9 - x^9 + x^8 - x^8 + x^7 - x^7 + x^6 - x^6 + x^5 + x^5 - x^5 + x^4 - x^4 + x^3 - x^3 + x^2 - x^2 + x - x + 1
= (x^10 + x^9 + x^8) - (x^9 + x^8 + x^7) + (x^7 + x^6 + x^5) - (x^6 + x^5 + x^4) + (x^5 + x^4 + x^3) - (x^3 + x^2 + x) + (x^2 + x + 1)
= x^8 (x^2 + x + 1) - x^7 (x^2 + x + 1) + x^5 (x^2 + x + 1) - x^4 (x^2 + x + 1) + x^3 (x^2 + x + 1) - x (x^2 + x + 1) + (x^2 + x + 1)
= (x^2 + x + 1) (x^8 - x^7 + x^5 - x^4 + x^3 - x + 1)

\(x^8+x+1=x^8+x^7-x^7+x^6-x^6+x^5-x^5+x^4-x^4+x^3-x^3+x^2-x^2+x+1\)

\(=\left(x^8+x^7+x^6\right)-\left(x^7+x^6+x^5\right)+\left(x^5+x^4+x^3\right)-\left(x^4+x^3+x^2\right)+\left(x^2+x+1\right)\)

\(=x^6\left(x^2+x+1\right)-x^5\left(x^2+x+1\right)+x^3\left(x^2+x+1\right)-x^2\left(x^2+x+1\right)+\left(x^2+x+1\right)\)

\(=\left(x^2+x+1\right)\left(x^6-x^5+x^3-x^2+1\right)\)

a)\(\left(x^2+x+1\right)\left(x^6-x^5+x^3-x^2+1\right)\)

b)\(\left(x^2+x+1\right)\left(x^5-x^4+x^2-x+1\right)\)

c)\(\left(x^2+x+1\right)\left(x^5-x^4+x^3-x+1\right)\)

bn xem lại đề nhé!

mk nghĩ là \(x^8+x+1\) hoặc \(x^7+x^2+1\)

1) \(x^2.y^2-1\)

\(=\left(x.y\right)^2-1^2\)

\(=\left(x.y-1\right).\left(x.y+1\right)\)

Chúc bạn học tốt!