Question

The sum of the remainder obtained when (x^3+(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

Answer:

VALUE OF K = (-5)

Step-by-step explanation:

BY REMAINDER THEOREM,

Zero of (x-2) =>  (x-2)=0           =>x=2

Let p(x)=x^3+kx+8x+k

p(2) = (2)^3+k(2)+8(2)+k = 8+2k+16+k = 3k+24 (REMAINDER)

Zero of (x+1) => (x+1)=0           =>x=(-1)

p(-1) = (-1)^3+k(-1)+8(-1)+k = -1-k-8+k = -9 (REMAINDER)

ACCORDING TO QUESTION,

=> (3k+24)+(-9) = 0

=> 3k+24-9=0                    => 3k+15=0                       =>3k=(-15)

=> k=(-5)

Hence, The value of "k" is (-5)