Answer:
k = 4
Step-by-step explanation:
If x + 2 is a factor of the polynomial;
By the factor theorem, if we set x + 2 = 0, then make x the subject of the formula; if we substitute the value into the polynomial, the result we should have after calculating should be zero
So, we have it that;
x + 2 = 0
x = -2
Substitute into the polynomial and equate to zero
(-2)^3 - k (-2)^2 + 2(-2) + 7k = 0
-8 -4k -4 + 7k = 0
-12 -4k + 7k = 0
-12 + 3k = 0
-3k = -12
k = -12/-3
k = 4
