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.​

Answer 1

x - 2= 0

x= 2

by putting the value of x =2

x³ + k + 8x + k = 0

2³+ k + 8×2+k = 0

8 + 2k + 16 = 0

24 + 2k = 0

2k = - 24

k = -24/2

k = -12

or

x+ 1 = 0

x = - 1

by putting the value of x= -1

-1³+ k + 8 × -1 + k= 0

-1 + 2k - 8 = 0

-9 + 2k = 0

2k = 9

k = 9/2