Phân tích các đa thức sau đây thành nhân tử

Question

1. a³ - 7a - 6

2. a³ + 4a² - 7a - 10

3. a(b + c)² + b(c + a)² + c(a + b)² - 4abc

4. (a² + a)² + 4(a² + a) - 12

5. (x² + x + 1) (x² + x + 2) - 12

6. x⁸ + x + 1

7. x¹⁰ + x⁵ + 1

Answer 1

a(b+c)^2+b(c+a)^2+c(a+b)^2-4abc
= ab^2+bc^2+2abc+bc^2+ba^2+2abc+ca^2+cb^2+...
=ab^2+ac^2+bc^2+ba^2+ca^2+cb^2+2abc
=ab(b+c)+ac(b+c)+cb(b+c)+a^2(b+c)
=(b+c)[a(a+c)+b(a+c)]
=(a+b)(a+c)(b+c)

x^2 + x + 1 = t
t(t + 1) = 12
t^2 + t - 12 = 0
(​x^2 + x + 1- 3)(​x^2 + x + 1 + 4) = 0
(​x^2 + x - 2)(​x^2 + x +5) = 0

 x8 + x + 1
= x^8-x^2+x^2+x+1
= x^2(x^6-1)+x^2+x+1
= x^2(x^3+1)(x^3-1)+ x^2+x+1
=(x^2+x+1)(x^2(x^3+1)(x-1)+1)

A= x^10 + x^5 + 1
A= (x^10 -x) + (x^5-x²) + (x²+x+1)
A= x.(x³ -1).(x^6+x³+1) + x².(x³-1) + (x²+x+1)
A= x.(x -1).(x²+x+1).(x^6+x³+1) + x².(x-1).(x²+x+1) + (x²+x+1)
A= (x²+x+1).[x.(x-1).(x^6+x³+1) + x².(x²+x+1) +1]