how do i factor this out x^2+4x+5

Question

Factor it out 

Answer 1

First, use the quadratic formula:

 

x = (-b ± √(b² - 4ac)) / 2a

 

where:

a = 1

b = 4

c = 5

 

x = (16 ± √(16 - 20)) / 2

x = (16 ± √(-4)) / 2

x = (16 ± 2i) / 2

x = 8 ± i

 

x = 8 - i             and             x = 8 + i

 

You have a complex solution.  We can turn these solutions into a product of factors.  We get

 

(x - [8 - i])(x - [8 + i]) =

 

(x - 8 + i)(x - 8 - i)