Question

How do you factor completely: `x^2 − 2x + 5`?

Answer 1

`x^2-2x+5 = (x-1+2i)(x-1-2i)`
`color(white)("XXXX")`(there are no Real factors for the given expression)

Explanation:

Write the expression as an equation with the expression equal to zero.
`color(white)("XXXX")` `x^2-2x+5 = 0`
Us the quadratic formula to determine the roots:
`color(white)("XXXX")` `(-b+-sqrt(b^2-4ac))/(2a)`
becomes
`color(white)("XXXX")` `1+-2i`

That is
`color(white)("XXXX")` `(x - (1+2i))*(x-(1-2i)) = 0`

So
`color(white)("XXXX")` `(x-1-2i) and (x-1+2i)` are factors of the the given expression.