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) 
----------------------- 
Phương pháp: 
Khi gặp bài toán phân tích thành nhân tử dạng x^(3m + 1) + x^(3n + 2) + 1 em thêm bớt các hạng tử từ bậc cao nhất trừ đi 1 đến x (bậc nhất) sao cho tổng số các hạng tử trong đa thức mới là một bội của 3. Sau đó nhóm ba hạng tử một sao cho trong mỗi nhóm có x² + x + 1 
Dạng này khi phân tích luôn có kết quả là: (x² + x + 1).Q(x)

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

1)a) x^2(x+1) - x(x-1)

=x.[x(x+1)-(x-1)]

=x.(x²+x-x+1)

=x.(x²+1)

b) 5(a-b)^2 - (a+b).(b-a)

=5(a-b)²+(a+b)(a-b)

=(a-b)[5.(a-b)+(a+b)]

=(a+b)(5a-5b+a+b)

=(a+b)(6a-4b)

=2(a+b)(3a+2b)

1) xem lại đề

a) \(x^5+x-1\)

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

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

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

\(=\left(x^2-x+1\right)\left(x^3+x^2-1\right)\)(còn 1 cách nữa là thêm bớt \(x^2\)vào bạn nhé!)

b) \(x^7+x^2+1\)

\(=x^7-x+x^2+x+1\)

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

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

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

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

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

(Chúc bạn học tốt và nhớ tíck cho mình với nhé!)

a) \(x^5-x^4-1\)

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

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

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

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

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

b) \(x^8+x^7+1\)

\(=\left(x^8-x^2\right)+\left(x^7-x\right)+\left(x^2+x+1\right)\)

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

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

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

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

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

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

a) \(x^5-x^4-1=x^5+x^2-x^4-x^2-1\)

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

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

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

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

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

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

b) \(x^8+x^7+1=x^8+x^7+x^6-x^6+1\)

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

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

\(=\left(x^2+x+1\right)\left[x^6-\left(x-1\right)\left(x^3+1\right)\right]=\left(x^2+x+1\right)\left(x^6-x^4+x^3-x+1\right)\)

Mong cô Chuy cho e thêm 1 Gp nựa nha cô '-'

\(x^7+x^2+1\)

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

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

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

a) \(x^7+x^2+1=\left(x^7-x\right)+\left(x^2+x+1\right)\)

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

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

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

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

b) \(x^7+x^5+1=\left(x^7+x^6+x^5\right)-\left(x^6-1\right)\)

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

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

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

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

\(x^5+x+1\)

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

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

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

ủa phần a mình phân tích rồi mà bạn hu hu