Answer
Zeros, each multiplicity 1:
$1+i, 1-i$
Factorization:
$P(x)=(x-1-i)(x+1+i)$
Work Step by Step
$x^{2}+2x+2=0$
Quadratic formula:
$x=\displaystyle \frac{-b\pm\sqrt{b^{2}-4ac}}{2a},\quad a=1, b=2, c=1$
$x=\displaystyle \frac{-2\pm\sqrt{4-4(1)(2)}}{2(1)}=\frac{-2\pm\sqrt{-4}}{2}$
$=\displaystyle \frac{-2\pm 2i}{2}=\frac{2(-1\pm i)}{2}=-1\pm i$
Zeros, each multiplicity 1:
$1+i, 1-i$
Factorization:$ 1[x-(1+i)][x-(1-i)]=$
$P(x)=(x-1-i)(x+1+i)$
