When $5 x^{13} + 3 x^{10} - k$ is divided by $x + 1$ , the remainder is 20. The value of k is

-22

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-12

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Solution

The correct option is A -22
Given,

when $5 x^{13} + 3 x^{10} - k$ is divisible by $x + 1$ , the remainder is $20$

let $f (x) = 5 x^{13} + 3 x^{10} - k$

$x + 1 \Rightarrow x = - 1$

$\Rightarrow f (- 1) = 20$

$\Rightarrow 5 (- 1)^{13} + 3 (- 1)^{10} - k = 20$

$5 (- 1) + 3 (1) - k = 20$

$- 5 + 3 - k = 20$

$- 2 - k = 20$

$- k = 22$

$∴ k = - 22$

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