Answer
$p(x)=x^3-2x^2-x+2$
Work Step by Step
From the graph, the polynomial function intercepts the x-axis at $x=-1,1,$ and $2$.
Then, the zeros are $-1,1$, and $2$.
In addition, the polynomial function also intercepts the y-axis at $y=2$, so the constant term is 2.
The polynomial has the general form $p(x)=A(x+1)(x-1)(x-2)$.
That is,
$p(x)=A(x^2-1)(x-2)$
$p(x)=A(x^3-2x^2-x+2)$
$p(x)=Ax^3-2Ax^2-Ax+2A$
Since the constant term is $2$, it must be $2A=2\to A=1$.
Therefore, $p(x)=x^3-2x^2-x+2$.
