x(x+2)(x+5)(x+7)+24=[x(x+7)][(x+2)(x+5)]+24=(x^2+7x)(x^2+7x+10)+24=(x^2+7x)^2+10(x^2+7x)+24=[x^2+7x)+4)][(x^2+7x)+6)]=(x^2+7x+4)(x^2+7x+6)=(x^2+7x+4)(x+1)(x+6).