Hey everyone, it's Justin again. In this unit we're going to be learning about multiplying and
factoring. Nope, not numbers. We're going to be multiplying and factoring entire algebraic
expressions. I know, sounds weird and difficult, but by the time you finish this unit it will be
just as easy as graphing a line. To start off, this video is going to teach you the
terminology that we're going to be using. At the end of this lesson, you will be able to describe
polynomials and their features using mathematical terminology. To reach that objective,
first you'll learn what a polynomial is and the names for different types of polynomials. Then
I'll teach you about standard form and how to find a polynomial's degree. Finally we'll finish with
a couple of practice examples. First, the most common term you'll probably hear throughout this
unit is polynomial. A polynomial is one or multiple terms, consisting of a coefficient,
multiplying a variable, raised to some power, being added or subtracted from one another.
That's a long definition, so let's break it down. A polynomial can be either one or multiple terms,
and those terms consist of a variable raised to some power and multiplied by a coefficient, added
or subtracted to one another. Oh okay, so this would be an example of a polynomial,
or this, or even this. Actually, a polynomial like this one has a very special name. It's called
a monomial. Mono means one, so a monomial is a polynomial with only one term. So what would we
call a polynomial with two terms? Bi like bicycle means two, so we call a polynomial with two terms
a binomial. And likewise, a polynomial with three terms is called a trinomial. We mathematicians
got kind of lazy after that. We just decided that anything with more than three terms would all be
lumped together under the general term polynomial. All those polynomials we've been using as examples
look weird, because there's no real organization to them. That's why we always try to neaten them
up by putting them in what is called standard form. Standard form is when all the terms are
arranged so that the exponents are in descending order, counting down. If an exponent is missing,
we just skip over it. Remember, adding and subtracting is connected to whatever comes
after it. So if you need to rearrange the terms, make sure each term keeps its sign.
Finally, every polynomial has a degree. The degree is the largest amount of variables being
multiplied in a single term. In standard form this is super easy to find. You just check the first
term which automatically has the biggest exponent. In this term there are eight x's being multiplied
together. So the degree of the polynomial is eight. When the polynomial isn't in standard form,
it's a little harder because you have to go looking for the biggest exponent. The degree
of this polynomial is nine. We won't be focusing too much on polynomials like this. At least not
in Algebra 1. But some polynomials use multiple variables. The degree here is determined by the
total amount of variables on the largest term, no matter what variables they are. The largest term
in this polynomial has four x's and nine y's for a total of 13 variables. So this is a degree 13
polynomial. Let's practice with a couple of examples. First, what type of polynomial is this?
This is a binomial because it has two terms. So how would we write it in standard form?
If you said it already is, then you're right. The exponents are already
in descending order. What's the degree of this binomial?
This binomial is degree three, because the largest term includes three x's multiplying together.
Next one, what's the name of this type of polynomial?
This type of polynomial is just called a polynomial,
and nobody ever said mathematicians were creative. So how would we write it in standard form?
In order of descending exponents, 7,
5, 2, and none. Don't forget to keep each term's sign. Finally, what degree is this polynomial?
This is a degree 7 polynomial.
Make sure to practice these definitions. Once you've mastered them, we can get to work learning
how to multiply polynomials together. Don't worry. In the next lesson we're going to start
by using visual models so that you can actually see how the multiplication works. See you then!