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)
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 )
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)