Hi kenny1999,

I will assume that you are talking about factoring quadratics, am I right?

A lot of teachers use the 'guess and check' method especially when the leading coefficient is 1. This takes a little more time when that coefficient is something other than 1.

Here's how I approach those. You might find it useful.

First a simple one:

Step 1: Multiply the leading coefficient (2) times the constant (3) to get (6).

Step 2: Determine (mentally) what two factors make (6) that also add up to the middle coefficient (7). You can quickly come up with (6) and (1).

Step 3: Replace the original middle term with these two values from Step 2.

Step 4: Factor by grouping

Here's a second one:

Step 1: 6 times -6 = -36

Step 2: With a little thinking, I can come up with -4 and 9 as my two factors that add up to +5.

Step 3:

Step 4:

I hope this is helpful to you and your students. It works for mine.