So, you’d think that combining a positive number and a negative number would be a fairly straightforward thing, huh?
Well, unfortunately, a lot of students think it’s easy. They think it’s too easy. They think there’s one simple rule that guides them to the very same kind of answer every time. And that’s exactly where they get into trouble.
The truth is that combining a positive and a negative number is a fairly complicated operation, and the sign of the answer is dependent on a nmber of factors.
This video reveals a common mistake students make when tackling these problems. it also shows the correct way to approach these problems, using the analogy of having money and owing money to make everything make sense.
So take a look and see if this explanation doesn’t end the confusion once and for all.
And don’t forget: there are practice problems at the end of the video. Do those to make sure you’ve grasped the concept.
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.