EXAMPLE:
x² + 7x + 12
My goal (x )(x )
I need two numbers that multiply to give 12 (the number by itself in the quadratic)
and add to give 7 ( the number before the x term)
So write factors of 12 - 1,12 or 2,6 or 3,4 or -1,-12 or -2,-6 or -3,-4.
Which pair adds to give 7?
3 and 4!
So we discovered that the factors of 12 that added to give 7 were 3 and 4
So we write
(x + 3)(x + 4)
We could write (x + 4)(x + 3)
Check your work by expanding!