Answer:
8
Step-by-step explanation:
[tex] \because \: p(x) \: is \: divisible \: by (x + 2) \\ \therefore \: x + 2 = 0 \implies \: x = - 2 \\ plug \: x = - 2 \: in \: p(x) \\ p( - 2) = 4 {( - 2)}^{3} + c {( - 2)}^{2} + ( - 2) + 2 \\ p( - 2) = 4 ( - 8) + 4c - 2 + 2 \\ p( - 2) = - 32 + 4c \\ let \: p(x) = 0.. (\because remainder = 0)\\ \therefore \: 0 = - 32 + 4c \\ \therefore \: 32 = 4c \\ \therefore \: c = \frac{32}{4} \\ \huge \red{ \boxed{\therefore \: c = 8}}[/tex]
