方法一:
x^4-10x^3+35x^2-50x+24
=(x^4-10x^3+9x^2)+(26x^2-50x+24)
=x^2(x^2-10x+9)+2(13x^2-25x+12)
=x^2(x-1)(x-9)+2(x-1)(13x-12)
=(x-1)[x^2(x-9)+2(13x-12)]
=(x-1)(x^3-9x^2+26x-24)
=(x-1)[(x^3-2x^3)-(7x^2-14x)+(12x-24)]
=(x-1)[x^2(x-2)-7x(x-2)+12(x-2)]
=(x-1)(x-2)(x^2-7x+12)
=(x-1)(x-2)(x-3)(x-4)
方法二:
x^4-10x^3+35x^2-50x+24
=x^4-(10x^3-10x^2)+(25x^2-50x+25)-1
=x^4-2x^2(5x-5)+(5x-5)^2-1
=[x^4-2x^2(5x-5)+(5x-5)^2]-1
=(x^2-(5x-5)]^2-1
=(x^2-5x+5)^2-1
=[(x^2-5x+5)-1][(x^2-5x+5+)1]
=(x^2-5x+4)(x^2-5x+6)
=[(x-1)(x-5)][(x-2)(x-3)]
=(x-1)(x-2)(x-3)(x-4)