Question

(x-1)(x-2)(x-3)(x-4)-24

Answer 1

(x-1)(x-4)(x-2)(x-3) -24 = (x^2-5x+4)(x^2-5x+6) -24 设y=x^2-5x,则 原式=(y+4)(y+6) -24 = y^2+10y+24-24 = y^2+10y = y(y+10) = (x^2-5x)(x^2-5x+10) = x(x-5)(x^2-5x+10)