What is the value of k , if (x + 1) is a factor of $$x^8 + kx^3 - 2x + 1$$​ ?

Correct option is D

Given:

(x+1) is a factor of  $$x^8 + kx^3 - 2x + 1$$​​

Concept Used:

If (x + 1) is a factor of a polynomial f(x), then by the Factor Theorem,

f(-1) = 0

Solution:

​$$f(x) = x^8 + kx^3 - 2x + 1$$​​

​$$f(-1) = (-1)^8 + k(-1)^3 - 2(-1) + 1 = 0$$​​

1 + (-k) + 2 + 1 = 0

4 - k = 0

k = 4