Question

The sum of the remainders 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

The statement means the sum of $\sf{p(2)}$ and $\sf{p(-1)}$ is zero by remainder theorem for $\sf{p(x)=x^3+(k+8)x+k.}$

So,

$\longrightarrow\sf{p(2)+p(-1)=0}$

$\longrightarrow\sf{(2)^3+2(k+8)+k+(-1)^3-(k+8)+k=0}$

$\longrightarrow\sf{8+2k+16+k-1-k-8+k=0}$

$\longrightarrow\sf{3k+15=0}$

$\longrightarrow\sf{\underline {\underline {k=-5}}}$

Answer 2

hope it helps!!!!!

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