yego.me
💡 Stop wasting time. Read Youtube instead of watch. Download Chrome Extension

Finding zeros of polynomials (2 of 2) | Mathematics III | High School Math | Khan Academy


2m read
·Nov 11, 2024

  • [Voiceover] In the last video, we factored this polynomial in order to find the real roots. We factored it by grouping, which essentially means doing the distributive property in reverse twice. I mentioned that there's two ways you could do it. You could actually, from the get-go, add these two middle degree terms, and then think about it from there.

So, what I thought I'd do is just a quick video on that alternative. If we add, instead of grouping, if we add these middle two terms. Actually, I'll just focus on the fourth degree polynomial here. We know that we have an x out front. This fourth degree polynomial is going to simplify to x to the fourth plus seven x squared minus 18. If we want to factor this, we could recognize a pattern here.

You probably remember. Hopefully, you remember. If you don't, then you might want to review your factoring polynomials. But if you have x plus a times x plus b, that's going to be equal to x squared plus the sum of those two numbers, a and b, as being the coefficient of the x term plus the product of those two numbers. If you just multiply this out, this is what you would get.

But if this was x squared plus a times x squared plus b, instead of this being x squared, this would be x to the fourth. Instead of this being x, this would be x squared, which is exactly the pattern we have here. So, what two a's and b's that if I add them up, I would get seven, and if I were to take their product, I get negative 18?

Well, since their product is negative, we know that they are of different signs. One will be positive, one will be negative. And since their sum is positive, we know that the larger of the two numbers is going to be positive. So, what jumps out at me is nine times negative two. You multiply those, you get negative 18. You take their sum, you get seven.

So, we can rewrite this, just looking at this pattern here as x squared plus nine times x squared minus two. I could say plus negative two. That's the same thing as x squared minus two. And then, that's exactly what we got right over here. Of course, you have this x out front that I didn't consider right over here.

And then, this, as we did in the previous video, you could recognize as a difference of squares and then factor it further to actually find the roots. But I just wanted to show that you could solve this by regrouping, or you can solve this by, I guess you could say, more traditional factoring means. And notice this nine and negative two, this is what was already broken up for us, so we could factor by regrouping.

More Articles

View All
The Challenges a Repeat Founder Faces - Tikhon Bernstam
Hey guys, today we have Tea Con Burn, a multi-time YC founder. So could you just start by explaining how you first found YC? Yeah, I actually found YC because I was on Reddit. I was in graduate school, which meant I had a lot of free time. And so I was, …
How to Sell Anything by Tony Robbins *rare video
So all you have to do to persuade someone is do two simple things. One, you have to identify, and ideally that first step you’re going to do is you’re going to identify the buying state. One, and two, is you’re going to anchor it—anchor that state to your…
Visually dividing decimal by whole number
In this video, we’re going to try to figure out what 4 tenths divided by 5 is. So pause this video and see if you can think about it before we work through it together. We’re really going to think about approaching this visually. All right, now let’s wor…
Creating a Food Forest | Farm Dreams
[Music] Oh, there’s baby chicks! Yep, two weeks old. I’ve gotta hold them. Hi, little friend! I sent Bob some photos and a description of Jill and Craig’s seven-acre plot, hoping he can offer advice on the best way to actualize their vision. Okay, this …
Turns Out, Caterpillar Fungus is Crunchy | Primal Survivor
[Music] Traditional doctors or amches are highly respected and regularly consulted. Here, their methods have been passed down from generation to generation. They are reputed to be able to transform Mountain herbs into remedies to treat everything from art…
Jeff Clavier and Andrea Zurek - Startup Investor School Day 3
Jeff is someone that I met in the very beginning of my venture into venture. When I first started investing a long time ago, he taught me as many lessons about how to be a good investor. In two senses, how to be a good investor by making good choices and …