Question

by factor theorem determine the value of k for which x+2 is a factory of (x+1)^7 + (2x+k)^3

Answer 1

If x+2 is factor of given polynomial then x=-2 is a root of equation (x+1)^7 +
(2x+k)^3=0.
So (-2+1)^7+(k-4)^3=0
(k-4)^3=1
k-4=1
k=5