If $x^{100} + 2 x^{99}$ + k is divisible by (x+ 1) = 0, then the value of k is

-3

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-2

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Solution

The correct option is D 1
Given that,
$x^{100} + 2 x^{99} + k$ is divisible by (x + 1)
Putting x = -1 in equation,
So, the remainder obtained by putting x = -1 in the expression will give remainder as 0.
$(- 1)^{100} + 2 (- 1)^{99}$ + k = 0
1 -2 + k = 0 $\Rightarrow$ k = 1

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