Yep, factoring quadratic trinomials is a key skill for Algebra 1. And the process can seem intimidating, especially at first.
But it’s actually surprisingly easy if taught in a certain way. And of course, that’s what I’m going to do here … teach it in the easiest and fastest way possible.
Believe it or not, there’s a reason teachers make you factor trinomials. They may not have told you yet, but they do this so you can solve equations with quadratic trinomials. Once you can factor one of these little beasts, solving an equation that contains one becomes amazingly simple. But without the ability to factor the trinomial, solving it is much more difficult.
You’ll notice that this video starts with four preliminary concepts. These are pretty simple concepts, and for most of you these will feel like review. But make sure you know all of those concepts before you go on, especially the concept of absolute value.
With these preliminaries “under your belt,” factoring trinomials will be rather easy.
To put this video into perspective, it shows how to factor two of the four kinds of quadratic trinomials, those with the pattern of + + + and + – +. After this video, I will post another that shows how to factor quadratic trinomials with the patterns of + + – and + – –.
Also, my first two videos on factoring trinomials are for trinomials whose a-value = + 1. There’s a different, more complicated process for factoring quadratic trinomials whose a-value is not = + 1. I’ll go over that in a few later videos.
In any case, this will get you started in a way that shouldn’t feel too painful. Follow along and good luck.
Ever thought this after you got back a math test … ?
“Why did I do that? I used a rule where it doesn’t apply!”
Yep, that’s exactly what we’re looking at in Algebra Mistake #3, a case of “overgeneralizing.”
The situation we’re dealing with involves over-generalizing everyone’s “favorite” property, the distributive property!
How’s that? Well, you’re supposed to use the distributive property when a number multiplies terms inside parentheses.
But sometimes students get a little bit — shall we say — “carried away” — and use the distributive property principle in other situations, too. The results are a tad bit comic, if you’re the teacher, but not so funny if you’re the student and you’ve made the mistake 19 times on a test with 20 problems.
Anyhow, after you watch the following video you shouldn’t have to worry about this again because we’ll get the two wires in your mind untangled so you never make this mistake again. So just relax, watch and learn.
And oh yes, don’t forget that we’ve provided some practice problems at the end of the video to help you make sure you’ve got the concept nailed down.
Now that you’ve gotten a taste for the benefits of analyzing algebraic mistakes, it’s time to explore a second common mistake. This one is so common that nearly every student commits it at least once on the road to algebra success.
As you watch the video, notice how by thinking hard about two expressions, we can think this mistake through to its very root, thus discovering the core difference between two similar-looking algebraic expressions.
And along the road, we’ll learn a general strategy for decoding the meaning of algebraic expressions. What I like about this strategy is that you can use it to understand the meaning of pretty much any algebraic expression, and you’ll see that it’s not a hard thing to do. In fact, it just involves using numbers in a nifty way.
Best of all, students usually find this approach interesting, convincing and even a bit fun. So here goes, Common Algebra Mistake #2 …