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

-8 will be your answer

Answer 2

Answer: The value of k is -11.

Step-by-step explanation:

Since we have given that

$x^3+(k+8)x+k$

First we divide the above polynomial by (x-2)

Using "Remainder theorem":

$x-2=0\\\\x=2$

It becomes,

$p(2)=2^3+(k+8)\times 2+k\\\\=8+2k+16+k\\\\=24+3k$

similarly, If we divide the above polynomial by x+1.

$x+1=0\\\\x=-1$

so, it becomes,

$p(-1)=-1^3+(k+8)\times -1+k\\\\=-1-k-8+k\\\\=-9$

Sum of remainder is 0.

So, it becomes,

$24+3k+9=0\\\\33+3k=0\\\\3k=-33\\\\k=\frac{-33}{3}\\\\k=-11$

Hence, the value of k is -11.