x² - x - 12
Start by setting up your two sets of parenthses.
X² breaks down into x and x.
What we are looking for is factors of the constant term
that add to the coefficient of the middle term.
The question is, what is the coefficient of the middle term
in this problem if there is nothing written in front of the x.
Well if there is nothing written there,
the coefficient is understood to be 1.
So what we are looking for are factors of -12 that add to -1.
Factors of -12
+12 · -1
-12 · +1
+6 · -2
-6 · +2
+4 · -3
-4 · + 3
We can see that -4 and +3 add to -1.
So they go in the second position of each binomial.
This gives us (x - 4)(x + 3) as our answer.
