Write x squared + 2x-8 in the form (x + m) squared + n where m and n are integers.

Let F (x) = x^2 + 2x - 8

Adding 1 and - 1 at equation

F (x) = x^2 + 2x + 1 - 1 - 8

Rewrinting the first 1 = 1^2

F (x) = x^2 + 2x + 1^2 - 1 - 8

Now look:

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

Then,

F (x) = (x + 1) ^2 - 1 - 8

F (x) = (x + 1) ^2 - 9

This is the answer!

If us to want.

(x + 1) ^2 - 9 = (x+1) ^2 - 3^2

= (x + 1 - 3). (x + 1 + 3)

= (x - 2). (x + 4)