# How do you factor  x^2-2x+2 ?

#### Responda:

This quadratic only factors with the help of Complex coefficients:

x^2-2x+2 = (x-1-i)(x-1+i)

#### Explicação:

x^2-2x+2

Isto está na forma ax^2+bx+c com a=1, b=-2 e c=2

It has discriminant Delta given by the formula:

Delta = b^2-4ac = (color(blue)(-2))^2-4(color(blue)(1))(color(blue)(2)) = 4 - 8 = -4

Desde Delta < 0, this quadratic has no Real zeros and no linear factors with Real coefficients.

We can still factor it, but we need to use Complex coefficients.

A^2-B^2 = (A-B)(A+B)

To factor our quadratic, we can complete the square and use the difference of squares identity with A=(x-1) e B=i como se segue:

x^2-2x+2 = x^2-2x+1+1

color(white)(x^2-2x+2) = (x-1)^2+1

color(white)(x^2-2x+2) = (x-1)^2-i^2

color(white)(x^2-2x+2) = ((x-1)-i)((x-1)+i)

color(white)(x^2-2x+2) = (x-1-i)(x-1+i)