Long ago I had a math teacher who showed us how to factor Polynomials without guessing. Can't recall how?

Question

I think he multiplied the equation and later divided out his multiplier. It was long ago.

Answer 1

If you have ax² + bx + c, then one way is to start with the factors of a*c.

For example if you had:
2x² + 13x - 7

You would start with the factors of -14:
-14 x 1
-7 x 2
-2 x 7
-1 x 14

Then you would sum each one:
-14 + 1 = -13
-7 + 2 = -5
-2 + 7 = 5
-1 + 14 = 13

As you can see, the one that gives you the value of b is the last one.

So that means you need to get -1 and 14 from the factors of a and c (2 and -7). a is obviously going to be 1 x 2 = 2, so write:
(2x ...)(x ...)

Since you have 1 * ? = -1 and 2 * ? = 14, you can quickly arrive at
(2x - 1)(x + 7)

Answer 2

Try http://www.purplemath.com/modules/factquad2.htm.

There is also a video podcast on itunes that shows another similar, yet a bit different, way.