Using Remainder or Factor Theorems to Find Coefficient I'm studying the remainder and factor theorems and a question asks:

-4 is a root of  $x^4 + ax^3 - 19x^2 - 46x + 120$  What is the value of a?

Since -4 is a root then I can deduce that x+4 is a factor of the polynomial. But that's as far as I get.
Hints?

The remainder theorem says if $a$ is a root of a degree $n$ polynomial $p(x)$, that is, if $p(a) = 0$, then $$(x-a) | p(x)$$ or equivalently, we can write $$p(x) = (x-a)q(x)$$ for some polynomial $q(x)$ with degree $n-1$.  
However, you don't need to apply that here.  If $-4$ is a root, then $p(-4) =  0$.  If you evaluate your polynomial for $x=-4$ you get an equation with $a$ as unknown.  
What is this equation?  
You can then solve it for $a$.
