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Math·Advanced Math·Nonlinear functions

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For a polynomial $p(x)$, the values are $p(2)=1$ and $p(4)=-1$. Which of the following must be true about $p(x)$?

A

$x-4$ is a factor of $p(x)$.

B

$x-1$ is a factor of $p(x)$.

C

$p(x)$ has a zero between $x=2$ and $x=4$.

D

The remainder when $p(x)$ is divided by $x-1$ is $2$.