Question

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

Answer 1

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)