Question

sum of remainders obtained when x³+(k+8)x+k is divided by (x-2) and when it is divided by (x+1) is zero.find k

Answer 1

f(x)=x^3+(k+8)x+k,
g(x)= x-2
h(x)= x+1
Take     x-2=0
             x=2
f(2)=8+(k+8)2+k
     =8+2k+16+k
     =24+3k

Take    x+1=0
            x=-1
f(-1)=-1+(k+8)(-1)-5
       =-1-k-8+k
       =-9
Now, Add the remainders
3k+24-9=0
3k+15=0
k=-5