#### Answer

$P(x)=[x-(i+4)][x+(i-4)]$
The zeros of the function are: $\{4+i,4-i\}$
$x =4+i$ with multiplicity 1
$x = 4-i$ with multiplicity 1

#### Work Step by Step

Factor the polynomial completely to obtain:
$P(x)=x^{2}-8x+17$
$P(x)=[x-(i+4)][x+(i-4)]$
Equate each unique factor to zero then solve each equation to obtain:
$x-(i+4)=0 \rightarrow x=4+i$
$x+(i-4)=0 \rightarrow x=4-i$
The zeros of the function are: $\{4+i,4-i\}$
$x =4+i$ with multiplicity 1
$x = 4-i$ with multiplicity 1