令别的因式是A
则x^4+mx³+nx-16=A(x-1)(x-2)
当x=1时x-1=0,所以右边=0
同理x=2时x-2=0,右边也等于0
所以x=1和2时,左边也等于0
x=1,x^4+mx³+nx-16=1+m+n-16=0
x=2,x^4+mx³+nx-16=16+8m+2n-16=0
所以m=-5,n=20
x^4-5x³+20x-16
=x^4-x³-4x³+4x²-4x²+20x-16
=x³(x-1)-4x²(x-1)-4(x-1)(x-4)
=(x-1)(x³-4x²-4x+16)
=(x-1)[x²(x-4)-4(x-4)]
=(x-1)(x-4)(x²-4)
=(x-1)(x-4)(x+2)(x-2)