(4-x²)(x-3)(x+1)
=-(x+2)(x-2)(x-3)(x+1)
=-(x+2)(x-3)(x-2)(x+1)
=-(x²-x-6)(x²-x-2)
=-[(x²-x)²-8(x²-x-6)+12]
=-[(x²-x)²-8(x²-x-6)+16-4]
=-[(x²-x)-4]²+4
易知对于任意实数x,都有：-[(x²-x)-4]²≤0成立,
那么：-[(x²-x)-4]²+4≤4
所以无论x取如何实数,(4-x²)(x-3)(x+1)≤4