SAT Question 4d425cef: Nonlinear Functions answer and explanation with Desmos solution

Choice C is correct. It's given that $f$ is a polynomial function and the graph of $y=f(x)$ in the xy-plane passes through the points $(-5,0)$, $(1,0)$, and $(4,0)$. A point in the form $(a,0)$ on the graph of $f(x)$ means that $x-a$ is a factor of $f(x)$. Since the graph of the function $f$ passes through the point $(1,0)$, $x-1$ must be a factor of $f(x)$.