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Math·Advanced Math·Nonlinear functions

hard

When the polynomial function $g$ is graphed in the xy-plane as $y=g(x)$, it passes through the points $(6,0)$, $(7,0)$, and $(0,13)$. Which of the following must be true?
I. When $g(x)$ is divided by $(x-6)$, the remainder is $0$.
II. The point $(7,0)$ is an x-intercept of the graph of $y=g(x)$.
III. When $g(x)$ is divided by $(x-13)$, the remainder is $0$.

A

II only

B

I and II only

C

I and III only

D

I, II, and III