Question

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

• A. 1
• B. -3
• C. 2
• D. -2

Answer 1

The correct option is A

1

Since $(x+1)$ is a factor, $x=-1$ will make the given expression zero.

$\therefore (-1{)}^{100}+2\times (-1{)}^{99}+k=0$
$\Rightarrow 1-2+k=0$
$\Rightarrow k=1$