Question

. Phân tích các đa thức sau đây thành nhân tử

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

4. Đặt  t= a^2 +a

Suy ra t^2 +4t - 12 = (t-2)(t+6) = (a^2+a-2) (a^2+a +6) = (a-1)(a+2)(a^2+a+6)

5. Đặt t = x^2 +x+1

Ta có: t(t+1) -12

= t^2 +t-12

= (t-3)(t+4)

= ( x^2 +x -2 ) (x^2+x+5)

 = (x-1) ( x+2) (x^2+x+5)

6. x^8 + x^7 + x^6 - x^7- x^6 - x^5 + x^5+ x^4 + x^3- x^4- x^3- x^2 + x^2 + x +1

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

7.  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^2 + x + 1) ( x^8 -x^7 + x^5 - x^4 + x^3 -x + 1)

Answer 2

         a³ - 7a - 6 

= a³ - a - 6a - 6 

= a ( a² - 1 ) - 6 ( a + 1 )

= a ( a - 1 ) ( a + 1 ) - 6 ( a + 1 )

= ( a + 1 ) [ ( a ( a - 1 ) - 6 ]

= ( a + 1 ) ( a² - a - 6  )

= ( a + 1 ) ( a² + 2a - 3a - 6 )

= ( a + 1 ) ( a + 2 ) ( a - 3 )

Answer 3

1. a³ - 7a - 6 

= a^3 - a - 6a - 6

= a(a^2 - 1) - 6(a + 1)

= a(a - 1)(a + 1) - 6(a + 1)

= (a+1)(a^2 - a - 6)

= (a+1)(a^2 -3a + 2a - 6)

= (a+1)[a(a-3) + 2(a-3)]

= (a+1)(a+2)(a-3)

2. a³ + 4a² - 7a - 10

= a^3 + 5a^2 - a^2 - 5a - 2a - 10

= a^2(a+5) - a(a+5) - 2(a + 5)

= (a^2 - a - 2)(a+5)

= (a^2 + a - 2a - 2)(a+5)

= [a(a+1) - 2(a+1)](a+5)

= (a+1)(a-2)(a+5)