(x+1)(x+2)(x+3)(x+4)-24
=[(x+1)(x+4)][(x+2)(x+3)]-24
=(x^2+5x+4)(x^2+5x+6)-24
=(x^2+5x)^2+10(x^2+5x)+24-24
=(x^2+5x)(x^2+5x+10)
=x(x+5)(x^2+5x+10)
(x+1)(x+2)(x+3)(x+4)-24
=[(x+1)(x+4)][(x+2)(x+3)]-24
=(x^2+5x+4)(x^2+5x+6)-24
=(x^2+5x)^2+10(x^2+5x)+24-24
=(x^2+5x)(x^2+5x+10)
=x(x+5)(x^2+5x+10)