SAT Question 0121a235: Nonlinear Functions answer and explanation with Desmos solution

Choice D is correct. According to the table, when $x$ is $-1$ or $2$, $p(x)=0$. Therefore, two $x$-intercepts of the graph of $p$ are $(-1,0)$ and $(2,0)$. Since $(-1,0)$ and $(2,0)$ are $x$-intercepts, it follows that $(x+1)$ and $(x-2)$ are factors of the polynomial equation. This is because when $x=-1$, the value of $x+1$ is $0$. Similarly, when $x=2$, the value of $x-2$ is $0$. Therefore, the product $(x+1)(x-2)$ is a factor of the polynomial function $p$.