Factor trinomials fast

Added: 2026-06-03

[00:00:00]All right, I've done a lot of videos on how to factor out trinomials when A values are one, being the number right there in front of the squared variable.

[00:00:09]But, what happens when that number is not one? So, there's a lot of rules on when it is one, but now we're talking about a number like three. So, the first thing you were going to do is just look and see, can three be factored out of all three terms? In this case, the answer is no.

[00:00:24]So, we're going to do what's called the AC method. So, you're going to say your A value, which is right here, the three, and your C value, which is the -5, you're going to take those two numbers and you're going to multiply them together.

[00:00:38]And I'm already writing the answer. So, 3 * -5 is equal to -15.

[00:00:44]So, what we're going to do is so we take the first number, the last number, multiply them together, and get this number. So, we have a -15. So, what I have done over here is write down factor pairs of -15. So, there's all four of them. And you're looking for the pair that adds up to that middle term, the B value, which in this case is -2.

[00:01:04]So, when I look at those pairs, the only pair that works to get me a -2 is this last pair right here. So, what we're going to do is we're going to write those out and separate them for the middle term. So, we're going to kind of separate the two things. So, the 3x² will become 3x² again.

[00:01:22]Then, in the middle here, we're going to separate it to the two that we just did, so three and -5. So, we're going to do a +3.

[00:01:29]And these are x's, so we're going to put that. And then the -5, put that as an x. And then we use that last term, which is the -5.

[00:01:38]And then we're going to do factor by grouping. So, what we're going to do is we're going to take this pair right here, if you have seen my videos on factoring by grouping, and then we're going to take this pair over here, and we're going to factor out what we can factor out.

[00:01:49]>> [snorts] >> In this side right here, you can factor out a three and an x. So, you're going to pull that out. And that what remains is a binomial right here. So, 3x * x would get me 3x squared.

[00:02:00]And then 3x * a 1 is going to keep that 3x.

[00:02:05]That's the first step. Then we're going to go over here. We're going to do that all over again. So, the number that we can factor out here is a -5.

[00:02:13]And how would I get a -5x? I'd have to multiply this by x. And then to get -5 * a negative what? Or to get what would be a -5 would be a +1.

[00:02:24]Now, this * this would give me this.

[00:02:27]This * this gives me that. And now you should see a pair of binomials that are the exact same right here. So, that is going to be what you're trying to do is make a binomial set that is identical.

[00:02:39]And then we have our numbers right here.

[00:02:41]We're going to take that and make that into our second binomial. And that is how we go ahead and factor when the number is not one. If you want more questions like this, find them on my YouTube, Instagram, and TikTok. If you want algebra, these are all located in the factoring trinomials playlist. Don't forget to like, share, follow me for more. Save it for later. I'll see you soon.