Today we're going to look at factoring trinomials. We can't use grouping in this situation, since there are only three terms, and we need four terms for grouping. This is why we need to learn some new methods. I want to look at these one at a time:
Our first method will help us factor polynomials in the form x^2 + bx + c, such as x^2 + 4x - 5 and x^2 - 6x + 9. I call this method unFOILing because it's doing the opposite of a technique called FOILing (First, Outer, Inner, Last), which you might remember from a previous class:
I have recorded several videos of worked-out example problems, which you can access at the link below. Once you start to get the hang of the problems, try them out before you watch the video to see if you're solving them correctly. And if you're not, compare your steps to those in the video to learn from your mistakes. This is a great opportunity for you to make sure you're doing each step correctly and mastering these skills!
Next we're going to factor polynomials in the form ax^2 + bx + c. This is different from the ones in the last section because of the a: these polynomials will have a leading coefficient other than 1! So we'll be looking at things like 3x^2 + 5x + 2 and 2x^2 - 19x + 35. In these cases, we have a leading coefficient that cannot be factored out as a GCF. So we'll need a different method here, and we call this the ac method.
Check out some example videos here: