Answer
Yes.
Work Step by Step
The factor theorem says that if f(c)=0, then (x-c) is a factor of f(x) and if (x-c) is a factor of f(x), then f(c)=0.
Hence $f(-7)=(-7)^4+5(-7)^3-19(-7)^2-29(-7)+42=2401-1715-931+203+42=0$, hence it is a factor of f(x).
