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Harder Trinomials - Undoing FOIL

Here's the best way to figure it out:

Make a list of possibilities... work through it until we hit the right one.

First Guys: 1 * 2 , Possible Last Guys: 1 *6 and 6 * 1 and 2 * 3 and 3 * 3 ... notice that I switched the order of the last guys to check all possible combos

Now, we just go through each one -- doing FOIL...

We need a middle guy of -x... So, -1

1) 1 * 2 and 1 * 6 ... the inner terms give 2 and the outer terms give 6 ... 2 and 6 cannot make a -1

2) 1 * 2 and 6 * 1 ... the inner terms give 12 and the outer terms give 1 ... 12 and 1 cannot make a -1

3) 1 * 2 and 2 * 3 ... the inner terms give 4 and the outer terms give 3 ... 3 - 4 = -1 ... we have a winner!