How do you factor a trinomial with no definite sum? Example: x^2-x-72. I've come up with about 12 different possibilities but when I check the answers in the back of the book, it only lists 1 possibility. So not sure what I'm doing wrong.

Question

anonymous · Answer

Use the Quadratic Formula! http://www.purplemath.com/modules/quadform.htm

hero · Answer

Well, you could use the guess and check method which is to find two numbers $m$ and $n$ that multiply to get $b$, yet add to get $a\dot\ c$: 

$m + n = -1$
$m \times n  = -72$

You'll find that only -9 and 8 will work

noreality11 · Answer

Thanks, now I understand :)

hero · Answer

You're welcome