Question

Factor the expression over the complex numbers.

x2+50

Answer 1

x² + 50

= x² - (-50)

=
`\sqrt{x^(2) } +/- √(-50)` Side note:
`√(-50) = √((-1) * 5 * 5) = 5i`

= (x + 5i)(x - 5i)

Answer 2

`(x+5i\sqrt 2)(x-5i\sqrt 2)`

Explanation:

We are given that an expression

`x^2+50`

We have to find the factor of given expression over the complex numbers.

Quadratic formula fro quadratic equation :
`ax^2+bx+c=0`

`x=(-b\pm√(b^2-4ac))/(2a)`

Using the formula

`x=(0\pm√(0-4(50)(1)))/(2)=(\pm i √(200))/(2)`

`x=(10i\sqrt 2)/(2), x=-(10i\sqrt2)/(2)`

`x=5i\sqrt 2, x=-5i\sqrt 2`

`x-5i\sqrt 2=0` and
`x+5i\sqrt 2=0`

Hence, the factor of
`x^2+50` is given by

`(x+5i\sqrt 2)(x-5i\sqrt 2)`