Question

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

Answer 1

(x-2) is the factor of the expression  x^3+(k+8)x +k

Let f (x) = x^3+(k+8)x +k

Putting x = 2 ( x - 2 is a factor)

f (2) = (2)^3 + (k+8)2+ k

         8 + 2k + 16 +k=0

         3k + 24 = 0

         3k = -24

         k = -24/3

         k = - 8

So the required expression becomes x^3 + (-8+8)x + k

Answer 2

first divide 1st no. with the dividend then divide it my second no. then you will get k=-33