(x-1)^3|x^4+ax^2+bx+c,求a+b+c的值

(x-1)^3|x^4+ax^2+bx+c,求a+b+c的值
(x-1)^3|x^4+ax^2+bx+c,求a+b+c的值

(x-1)^3|x^4+ax^2+bx+c,求a+b+c的值
已知,(x-1)^3|x^4+ax^2+bx+c ,
可设：x^4+ax^2+bx+c = (x+k)(x-1)^3 ,
可得：x^4+ax^2+bx+c = x^4+(k-3)x^3+(3-3k)x^2+(3k-1)x-k .
比较对应项系数可得：k-3 = 0 ,解得：k = 3 ,
则有：a = 3-3k = -6 ,b = 3k-1 = 8 ,c = -k = -3 ,
所以,a+b+c = -1 .