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
Why Does The Earth Spin?
So, I’m down in West Vancouver, British Columbia, which is where I grew up. At the local beach, there is this 2 and 1⁄2 ton granite sphere that was made to have a tolerance of 200s of a millimeter. This is an amazing granite sphere, and it’s floated on a …
Warren Buffett: How to Invest Small Amounts of Money
So it’s no secret that if you’re watching this video, you probably want to be a billionaire just like Warren Buffett. But believe it or not, if you have a relatively small amount of money in your portfolio, you actually have a huge advantage over Buffett …
15 Signs You’re Pre-Rich
Some of you aren’t broke, right? You’re just on the way to becoming rich. Let’s call you pre-rich. Your time hasn’t come yet, but you might share some of these early signs that one day, probably soon, your reality will match your potential. Here are 15 si…
PDSInvitation
Hi, Kevin Oerry here, businessman, investor, entrepreneur. You probably know me from ABC Shark Tank. I want to personally invite you to join me in Orlando for an exciting pharmacy industry event unlike any other that I’ll be speaking at in February: the 2…
Culture with Brian Chesky and Alfred Lin (How to Start a Startup 2014: Lecture 10)
The main stage is going to be with Brian when he comes up and talks about how he built the Airbnb culture. So you’re here, you’ve been following the presentations and now you know how to get started. You built the team, you started to sort of build your p…
Ask Sal Anything! Daily Homeroom Live: Monday, April, 27
Hi everyone! I’m Dan to you from Khan Academy. Unfortunately, after about a month and a half, Sal’s unable to join us today. But you do have myself and another kind of me team member, Megin Pattani, who’s here to kind of hold down the fort while Sal’s awa…