Question

if x+2 is a factor of( x+1)^5 + (2x+k)^3 find k

Answer 1

if x+2 is a factor of given polynomial.
putting x = -2 will make polynomial zero.
so
(-2+1)^5 + (-4+k)^3 = 0
-1 = -(k-4)^3
(k-4)^3 = 1
k-4 = 1
k = 5

Answer 2

p(x) = (x+1)^5 + (2 x +k)^3

given x+2 is factor

so x+2 = 0 & x= -2

p(x= -2) = (-2 + 1)^5 + (2(-2) +k)^3

   0      =   (-1)^5  + (-4 + k)^3

   0     =   -1  +(-4 +k)^3

(-4 + k)^3  = 1

(-4 + k)   = 1^3

-4 + k = 1

k = 1 + 4

k = 5