If x+2 is a factor of ${{(x + 1)}^{5} + (2 x + k)^{3}}$ , then the value of 'k' is

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Solution

The correct option is C 5
(x + 1)⁵ + (2x + K)³= 0
(-2 + 1)⁵ + [(2(-2)+ K)]³ = 0
(-1)⁵ + [-4 + k]³ = 0
-1 + [-4 + k]³ =0
(-4 +k)³= 1
-4+ k = 1
k = 1 + 4
k = 5

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