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 0. Find the value of K​

Answer 1

Step-by-step explanation:

x3+(k+8)x+k

Put x=2 to obtain first remainder

⇒R1=(2)3+(k+8)2+k=24+3k

Put x=−1 to obtain second remainder

⇒R2=(−1)3+(k+8)+k=−9

So R1+R2=0

⇒24+3k−9=0

⇒3k=−15

⇒k=−5.

Answer 2

Answer:

x

3

+(k+8)x+k

Put x=2 to obtain first remainder

⇒R

1

=(2)

3

+(k+8)

2

+k=24+3k

Put x=−1 to obtain second remainder

⇒R

2

=(−1)

3

+(k+8)+k=−9

So R

1

+R

2

=0

⇒24+3k−9=0

⇒3k=−15

⇒k=−5.