It is not a factor of $f(x).$
Work Step by Step
The Remainder Theorem says that the remainder when a function $f(x)$ is divided by $(x-r)$ is $f(r)$. Hence $f(-4)=4^7-64\cdot4^4-4^2-15=1\ne0$, therefore $(x+4)$ is not a factor of $f(x)$ by the factor theorem. The factor theorem says that if $f(c)=0$, then $(x-c)$ is a factor of $f(x)$ and vice versa.