Question

find all the zeros of the function. (enter your answers as a comma - separated list.)
$h(x)=x^{4}+6x^{3}+10x^{2}+6x + 9$
$x = $
write the polynomial as a product of linear factors. use a graphing utility to verify your results graphically. (if possible, use the graphing utility to ver
$h(x)=\boxed{(x + 3)^{2}(x - i)(x + i)}$

Explanation:

Step1: Identify factored form

We know $h(x)=(x+3)^2(x-i)(x+i)$

Step2: Set factors to 0

For $(x+3)^2=0$:
$x+3=0 \implies x=-3$ (double root)
For $(x-i)=0$:
$x=i$
For $(x+i)=0$:
$x=-i$

Answer:

$-3, -3, i, -i$