Question

The sum of the remainders obtained when (x3 + (k+8)x + k) is divided by (x - 2)
or when it is divided by (x + 1) is zero. Find the value of k.
a​

Answer 1

Answer:

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