Factoring Trinomials - Part 2
To factor a trinomial in the form of x squared plus bx plus c, we use the same exact method as the ac method. So, bear with me for a little while and then I’ll show you the shortcut. In order to use the ac method, we have to pick out what our "a" is, and in this scenario it doesn't look like there is anything in front of that squared. However, if nothing is in front of a variable, there is always an implied 1. What we are going to do using the ac method that we learned in a previous video, we are going ahead and multiply this 1 and this negative 15 together. So we have negative 15. The two numbers that add together to be negative 2 (the two factors that add together to be negative 2) is going to be negative 5 and 3. So these are the numbers we are going to use to split up this negative 2x. So, we are going to go ahead and bring down our x squared, and split up the negative 2x by saying negative 5x plus 3x, and then bring down the negative 15. Now all we have to do is group the first two terms together, and the last two terms together. Our greatest common factor in the first grouping is x. We are going to factor that out leaving us with x minus 5. The greatest common factor in the second grouping is a 3, so we are going to take that out as well. We are left with x minus 5. Again, here's a term and here's a term. Looks like the greatest common factor in both of those terms is x minus 5. We simply take that out leaving us with the x plus 3. So this is fully factored. The x minus 5 times x plus 3 is the factored form of this x squared minus 2x minus 15. Notice something. This negative 5 and positive 3 are the same magic numbers that we used to split up this negative 2 (and that's okay). So here's the shortcut. Anytime that you see a trinomial with the number 1 for its "a", you can automatically go ahead and write in your two parentheses, your x values in front (because you know you have to multiply these two guys together to give you this x squared). Then just use the factors of negative 15, which are negative 5 and positive 3. And again, if you want to, you can choose to make the x plus 3 first. It doesn't matter. It's the same exact thing. You won't get counted off for any of that.