1. The problem asks to determine an equation in factored form for a polynomial function given its graph. 2. From the graph, the polynomial crosses the x-axis at $x = -2$, $x = 0$, and $x = 1$. These are the roots of the polynomial. 3. The general factored form of a polynomial with roots $r_1$, $r_2$, and $r_3$ is: $$f(x) = a(x - r_1)(x - r_2)(x - r_3)$$ where $a$ is a constant coefficient. 4. Substituting the roots: $$f(x) = a(x + 2)(x)(x - 1)$$ 5. To find $a$, we would need another point on the graph, but since it is not provided, the equation in factored form is: $$f(x) = a(x + 2)x(x - 1)$$ 6. This form shows the polynomial has zeros at $-2$, $0$, and $1$, matching the graph. Final answer: $$f(x) = a(x + 2)x(x - 1)$$