Ta có :
$M=(x+2)(x+3)(x+4)(x+5)-24$
$=[(x+2)(x+5)][(x+3)(x+4)]-24$
$=(x^2+7x+10).(x^2+7x+12)-24$
$=(x^2+7x+10).[(x^2+7x+10)+2]-24$
$=(x^2+7x+10)^2+2.(x^2+7x+10)+1-25$
$=(x^2+7x+11)^2-5^2$
$=(x^2+7x+6)(x^2+7x+16)$
$=(x^2+x+6x+6)(x^2+7x+16)$
$=(x+1)(x+6)(x^2+7x+16)$
Vậy : $M=(x+1)(x+6)(x^2+7x+16)$