(x-1)(x-2)(x-3)(x-4)-3分解因式用换元法作，例;令x+y=t,

Question

(x-1)(x-2)(x-3)(x-4)-3分解因式
用换元法作，例;令x+y=t,

Answer 1

(x-1)(x-2)(x-3)(x-4)-3
=(x²-5x+4)(x²-5x+6)-3
令x²-5x=t
=(t+4)(t+6)-3
=t²+10t+24-3
=t²+10t+21
=(t+3)(t+7)
=(x²-5x+3)(x²-5x+7)
中间令x²-5x+5=t也可以
=(t-1)(t+1)-3
=t²-4
=(t-2)(t+2)
=(x²-5x+3)(x²-5x+7)
如果实数范围内分解的话
=(x-(5+√13)/2)(x+(5+√13)/2)(x²-5x+7)