Answer
$8(k+5)^2$.
Work Step by Step
The given polynomial is
$=8k^2+80k+200$
Factor out $8$.
$=8(k^2+10k+25)$
Write the the polynomial as $a^2+2ab+b^2$.
$=8(k^2+2(k)(5)+5^2)$
Use perfect square trinomial pattern
$a^2+2ab+b^2=(a+b)^2$
We have $a=k$ and $b=5$.
$=8(k+5)^2$
Hence, the factor of the given polynomial is $8(k+5)^2$.