Let D be a UFD. Show that a nonconstant divisor of a primitive polynomial in D[x] is again a primitive polynomial. Laying out the clues, I have $f(x), g(x) \in D[x]$. Assume that $g(x)|f(x) = c(x)$ such that $f(x) = c(x)g(x)$. 
Given that g(x) is a primitive polynomial, does this mean any factorization such that $f(x) = c(x)g(x)$ implies that c(x) is a unit in D and c(x)? is the "content"?
Expanding the notation of f(x), we have $f(x) = (c_1(x)c_2(x)...c_i(x))(g_1(x)g_2(x)...g_i(x))$.. then I'm not sure how to proceed from here.
Thanks in advance.

Saying that the factor is not primitive means that a prime/irreducible divides it: so $f(x)=pf_1(x)$ for some prime $p\in D$.
Thus $g(x)=pf_1(x)c(x)$ is not primitive.
