2) ( x + 2 )( x + 3 )( x + 4 )( x + 5 ) - 24
= (x2+7x+10)(x2+7x+12)−24
Đặt t = x2+7x+10 ta có :
= t( t + 2 ) - 24 = t2 + 2t - 24
= t2 - 4t + 6t - 24 = t(t-4) + 6(t-4)
= ( t-4 )(t+6)
= ( x2 + 7x + 10 - 4)( x2 + 7x + 10 + 6 )
= ( x2 + 7x + 6 ) ( x2 + 7x + 16 )
= ( x + 1 ) ( x + 6 ) ( x2 + 7x + 16 )