(x×x+3x+2)(x×x+7x+12)-24
=(x+1)(x+2)(x+3)(x+4)-24
=(x+1)(x+4)(x+2)(x+3)-24
=(x²+5x+4)(x²+5x+6)-24
=(x²+5x)²+10(x²+5x)+24-24
=(x²+5x)²+10(x²+5x)
=(x²+5x)(x²+5x+10)
=x(x+5)(x²+5x+10)