Answer:
[tex]x^2+72=(x-6i\sqrt{2})(x+6i\sqrt{2})[/tex]
Step-by-step explanation:
[tex]x^2+72[/tex]
To get the factors , first we solve the given expression for x
[tex]x^2+72=0[/tex]
Subtract 72 from both sides
[tex]x^2=-72[/tex]
Take square root on both sides
[tex]x=+-\sqrt{-72}[/tex]
square root (-1) is 'i'
[tex]x=+-i\sqrt{72}[/tex]
[tex]x=+-6i\sqrt{2}[/tex]
[tex]x=+6i\sqrt{2}[/tex] and [tex]x=-6i\sqrt{2}[/tex]
Write the x values in the parenthesis to get the factor form
When 'a' is a x value then (x-a) is a factor
[tex]x^2+72=(x-6i\sqrt{2})(x+6i\sqrt{2})[/tex]
