Operations with Polynomials in Several Variables

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• 0:02 A Polynomial with…
• 1:38 How to Add and Subtract
• 3:20 How to Multiply and Divide
• 4:03 Using Given Values
• 4:59 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

In this video lesson, you will learn how to handle and work with polynomials that have more than one variable. This is important because in math you sometimes have to work with several variables at the same time.

A Polynomial with Several Variables

In math, you won't always have the luxury of working with equations and functions that only have one variable. See, sometimes you will have equations and functions that have more than one variable.

In this video lesson, we will talk about what you can do when you have a polynomial with several variables. Recall that a polynomial is a function made up of terms connected by either a plus or a minus. Your terms are made up of a coefficient, the number part, and possibly a variable, the letter part.

You know very well how to evaluate the polynomial 4x + 5x. You know about like terms and so you can easily give an answer of 9x. And if we had 4x + 5x = 18, you can easily solve it for x to find that x = 2.

But, what will you do if we have a polynomial such as 4x + 2y + z = 0? This polynomial has several variables in it. Which one do you solve for? And, how do you do it? Keep watching and you will find out.

The good news is that in problems, they tell you which variable they want you to solve for. In our problem, we have three variables: x, y, and z. The problem will tell us which variable to solve for. Whenever you see several variables, don't always assume that you will solve for x. The problem might tell you to solve for y! Why don't we solve this problem for y? Let's see what happens.

How to Add and Subtract

To help me keep my variables straight, I like to think of them as different kinds of objects. I like food, so I think of my x's as French fries, my y's as burgers, and my z's as ice cream. This kind of visualization might also help you.

So for this problem, I am looking for burgers. I need to isolate my burgers so I can take a big bite out of them! I look at my polynomial and I see that I need to perform some subtraction to help me isolate my y variable.

We see that we have two terms that need to be moved to the other side. They have pluses in front of them, so to move them I need to subtract. If they have minuses in front of them, I would need to add to move them over. I am subtracting, so I will subtract first one term and then the other.

I remember that if I perform one operation on one side, I have to perform the same operation to the other. So, if I subtract 4x from one side, I also subtract it from the other. Doing this I get 2y + z = -4x.

Now, I need to subtract the z from both sides. Doing that I get 2y = -4x - z. Notice that the 4x and the z are not like terms so I can't combine them. Since I can't combine them, I leave them as they are and I just write them all out.

When you are working with several variables, don't worry about combining everything because when you have several variables you won't always be able to do that. It is perfectly okay to have a long answer with several variables.

How to Multiply and Divide

I'm not done with my problem, though. I still need to get my y by itself. I see that a 2 is multiplying it.

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