Question

pls...give me the solution of this image

Answer 1

$given \: \: {x}^{3} + (k + 8)x + k \\ \: remainder \: when \: divided \: by \\ (x - 2) \: is \: {2}^{3} + (k + 8) \times 2 + k \\ = 3k + 24 \\ remainder \: when \: divided \: by \\ (x + 1) \: is \: { - 1}^{3} + (k + 8) \times - 1 \: + k \\ = - 9 \\ sum \: of \: remainders \: = 0 \\ 3k + 24 \: - 9 = 0 \\ 3k = - 15 \\ k = - 5$