How do i factor this? please help :)

x^2+2x+5

x^2+2x+5
x(x+2)+5

You can simplify that thinking like this:

x^2+2x+c+d , when c+d = 5

solving the equation x^2+2x+c=0 for delta(polynomial discriminant)=0, you find the root=-1 for c=1

so now, you can right that: (x-1)^2+d and you know that d=4 because d+c=5 and c=1

so, you have now (x-1)^2+4

I don't know if that's good for you^^
Sorry for the english. I'm from Brazil and i'm practicing your language.
Bye