Question

The sum of remainder obtained when x 3 + (k+8)x +k is divided by x-2 and when it is divided by x+1 is 0 . Find the value of k.

Answer 1

Answer:

Step-by-step 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

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