a) ( x2 + x)2 + 4( x2 + x) - 12

Đặt : x2 + x = a , ta có :

a2 + 4a - 12

= a2 - 4 + 4a - 8

= ( a - 2)( a +2) + 4( a - 2)

= ( a -2)( a +6)

Thay x2 + x = a , ta có :

( x2 + x - 2)( x2 + x +6)

= ( x2 - x + 2x - 2)( x2 + x +6)

= [ x( x - 1) + 2( x - 1)]( x2 + x +6)

= ( x + 2)( x - 1)( x2 + x +6)

b) ( x2 + x + 1)( x2 + x + 2) - 12

Đặt x2 + x + 1 = a , ta có :

a.( a + 1) - 12

= a2 + a - 12

= a2 - 32 + a - 3

= ( a - 3)( a +3) + ( a - 3)

= ( a - 3)( a +4)

Thay x2 + x + 1 = a , ta có :

( x2 + x - 2)( x2 + x + 5)

= [ x( x - 1) + 2( x - 1)]( x2 + x + 5)

= = ( x + 2)( x - 1)( x2 + x + 5)

c) ( x2 + 4x + 8)2 + 3x( x2 + 4x + 8) + 2x2

Đặt : x2 + 4x + 8 = a , ta có

a2 + 3ax + 2x2

= a2 + ax + 2ax + 2x2

= a( a + x) + 2x( a + x)

= ( a + 2x )( a +x)

Thay x2 + 4x + 8 = a , ta có

( x2 + 6x + 8)( x2 + 5x + 8)