Answer
$f(x)=(x+5-2\sqrt 2)(x+5+2\sqrt 2)$
The zeros:
$x=-5+2\sqrt 2$
$x=-5-2\sqrt 2$
Work Step by Step
$x^2+10x+17=0~~$ ($a=1,b=10,c=17$):
$x=\frac{-b±\sqrt {b^2-4ac}}{2a}=\frac{-10±\sqrt {10^2-4(1)(17)}}{2(1)}=\frac{-10±\sqrt {32}}{2}=\frac{-10±4\sqrt 2}{2}=-5±2\sqrt 2$
$x=-5+2\sqrt 2$ or $x=-5-2\sqrt 2$
$f(x)=[x-(-5+2\sqrt 2)][x-(-5-2\sqrt 2)]=(x+5-2\sqrt 2)(x+5+2\sqrt 2)$
