Question

Factor the expression over the complex numbers.

x2+20

Answer 1

x²+20=0
x=±√(-80)/2
x=±4i√5/2=2i√5

factorised it is then
(x+2i√5)*(x-2i√5)

Answer 2

`x^2+20=(x-2√(5)i)(x+2√(5)i)`

Explanation:

Given : Expression
`x^2+20`

To find : Factor the expression over the complex numbers ?

Solution :

To factor we equate the expression to zero.

`x^2+20=0`

Subtract 20 both side,

`x^2+20-20=-20`

`x^2=-20`

Taking root both side,

`x=√(-20)`

`x=\pm 2√(5)i`

The factor of the expression is
`x^2+20=(x-2√(5)i)(x+2√(5)i)`