Question

fill in the blanks so that the polynomial will have a the behavior shown at each x - intercept.
( h(x) = -(x + square)^2(x + square)(x - square)^4 )

Explanation:

Step1: Identify x-intercepts from graph

The x-intercepts are $x=-4$, $x=-1$, $x=3$.

Step2: Match intercepts to factor form

For intercept $x=a$, factor is $(x-a)$. For $x=-4$: $(x+4)$ (matches squared term, even power touches axis). For $x=-1$: $(x+1)$ (odd power crosses axis). For $x=3$: $(x-3)$ (even power touches axis).

Step3: Fill blanks in polynomial

Substitute into $h(x)=-(x+\square)^2(x+\square)(x-\square)^4$.

Answer:

$h(x)=-(x+4)^2(x+1)(x-3)^4$
Blanks filled: 4, 1, 3 (in order from left to right)