Question

fill in the blanks so that the polynomial will have a the behavior shown at each x - intercept.
( g(x)=x^{2}(x + square)^{square} )

Explanation:

Step1: Identify x-intercepts from graph

The graph has x-intercepts at $x=0$ and $x=-2$.

Step2: Match intercept to factor form

For $x=-2$, the factor is $(x+2)$, so the first blank is 2.

Step3: Determine intercept behavior

At $x=-2$, the graph crosses the axis, so the exponent of $(x+2)$ is odd (choose 1, the simplest odd positive integer).

Answer:

$g(x) = x^2(x+2)^1$ (blanks filled with 2 and 1, respectively)