If $x^{140} + 2 x^{151} + k$ is divisible by x + 1, then the value of ‘k’ is___

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Solution

Let $f (x) = x^{140} + 2 x^{151} + k$ .
Since $f (x)$ is divisible by $x + 1$ , $f (1) = 0$
Put x=-1 in the given expression, we get
$(- 1)^{140} + 2 (- 1)^{151} + k = 0 \Rightarrow 1 - 2 + k = 0 \Rightarrow k = 1$

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