 This video will talk about the basics of polynomials. You need to know a few things about polynomials. See if we can fill in this table and learn a few things. So we want to know the type of polynomial. Well, it depends on how many terms we have. This particular one has four terms, so I'm going to put that in my number of terms over here. And if it's anything greater than three, we just call it a polynomial. So I'm just going to put poly in here. It has four terms. And then we want to talk about like terms. Well, in like terms, we have to have exactly the same variable and exponent on the variable. So I have three terms here that have x's in them, but none of them have the same exponent, so I don't have any like terms in this particular polynomial. Now, the degree of the polynomial. Degree of the polynomial is the largest exponent, or if we have more than one variable, the largest sum of the exponents on a term. So this one would be four, two, one, and be zero. I have four is my largest degree. Degree of the polynomial is four. And then the leading coefficient is just the coefficient on the term that had the largest exponent. In our case, we would say that the leading coefficient is three. And then in this one, I want to just see if it's simplified, but there are no like terms, so it can't be simplified. So it's done. All right, for our second one. Now we have three terms. And when you have three terms, that's what we call a trinomial. And that has three terms. And in this case, we do have some like terms because there's an x term here and there's also an x term here. So if I lift those like terms, I have three x, and I also have negative nine x. The degree of my polynomial is going to, again, be the largest exponent, and that happens to be two. So that's the degree of my polynomial. And then the coefficient on that term is my leading coefficient, and that's a positive two. And I can simplify this one. Two x squared stays because it has nothing like it, but I can take three x and subtract nine x, combine these two terms, and I get minus six x. This one is what we call a monomial. Mono means one. So it's a monomial, and we have one term. There are no like terms since I only have one. And the degree on this polynomial is going to be zero. The leading coefficient is that constant value that we see there. So it's negative nine. And again, there's no simplifying to be done because there were no like terms. We have one more kind of special kind of polynomial, and that's this one here. This is called a binomial because we have two terms. So we have monomial, binomial, trinomial, and after three, we just call them all polynomials. All of them are actually polynomials, but we give these three a special name. All right. So the number of terms gives us two. That's why it's a binomial. And do we have any like terms? No. Degree of the polynomial, the only one I see is this six. That would be the degree of my polynomial. And again, the coefficient on that thing, including the sign in front of it, will be my leading coefficient. So that's negative two. And since I didn't have any like terms, again, I can't simplify. Now, you may not be able to read this very well, but we have one, two, three, four terms. So this is just a polynomial. And we had, we said four terms. And it's, it is a b plus two a squared b plus three a b minus four a squared b squared. So if I look at that very closely, I have an a b term right here, and I have another a b term right here. So I have a b and I also have three a b. Now, the other two are not like terms because this one has an a squared, but only one factor of b in the term. And this one over here has the a squared, but it has two factors of b with it. So they're not like terms. All right. So the degree of the polynomial, this is where it gets fun. We have to add the exponents to know what the degree of each term is. So if we add the a and b, that's just going to be two. And if I had as a squared and b, that's two plus one or three. And this one again is two because it was like term. And then we have two plus two. So that makes for the degree of our polynomial. And again, just like before, the number in front of it including the sign. So it's a negative four. We can simplify this one. So I'm going to write my two a squared b. And then that combination, they're both positive. So I had three plus one more would be plus four a b. And then I'm going to have minus my four a squared b squared. And then my final one, it's two terms, so it's a binomial. There are no like terms. And now we have to add our exponents again to find our degree. Three plus four is going to be seven. And four plus two is going to be six. Seven is going to be the degree of my polynomial. The coefficient in front of that is just a one. So the leading coefficient would be one. And I had no like terms, so I can't simplify.