Question

Factor the expression over the complex numbers. x^2+72

Answer 1

x^2 = -72 so x is
`i*6√(2) or -i*6√(2)`

Answer 2

`x^2+72=(x-6i√(2))(x+6i√(2))`

Explanation:

`x^2+72`

To get the factors , first we solve the given expression for x

`x^2+72=0`

Subtract 72 from both sides

`x^2=-72`

Take square root on both sides

`x=+-√(-72)`

square root (-1) is 'i'

`x=+-i√(72)`

`x=+-6i√(2)`

`x=+6i√(2)` and
`x=-6i√(2)`

Write the x values in the parenthesis to get the factor form

When 'a' is a x value then (x-a) is a factor

`x^2+72=(x-6i√(2))(x+6i√(2))`