The sum of remainders obtained when x3+(k+8)x +k is divided by x-2 and when it is divided by x+1 is 0 fine the value of k

k=-5

Step-by-step explanation:

The remainder theorem says that for any polynomial p(x) , if we divide it by the binomial x−a , the remainder is equal to the value of p(a) .

Therefore for if it is divided by x-2 and x+1 then its remainder must be p(2) and p(-1)

where,

According to the question,

p(2)+p(-1)=0