About This Chapter
AFOQT: Polynomials, Functions & Rational Expressions - Chapter Summary
Go through the lessons in this chapter to review imaginary numbers, complex numbers and polynomials. By the end of this chapter, you should be capable of answering questions on the AFOQT exam that deal with:
- Performing operations with complex numbers
- Adding, subtracting and multiplying polynomials
- Using long division and synthetic division to divide polynomials
- Identifying and solving problems with functions
- Composing functions and writing inverse functions
- Solving rational equations
- Multiplying and dividing rational expressions
The videos in this chapter are short and engaging, which can make studying for the test fun. After watching a video, take its corresponding quiz to test your skills and knowledge. If you still need to review a specific topic from this chapter, be sure to click on the video tags located at the bottom of each video.
1. What is an Imaginary Number?
The imaginary number 'i' is the square root of -1. Although this number doesn't actually exist, pretending that it does allows us to do a bunch of crazy math that scientists use every day. Learn the basics of that number 'i' here!
2. How to Add, Subtract and Multiply Complex Numbers
Knowing that complex numbers exist is the first step. But that knowledge alone won't help you do much with them. Learn the basics of complex number addition, subtraction and multiplication here!
3. How to Divide Complex Numbers
While adding, subtracting and multiplying complex numbers is pretty straightforward, dividing them can be pretty tricky. It comes down to the process of multiplying by the complex conjugate. Learn about what that is, and how to do it, here.
4. How to Add, Subtract and Multiply Polynomials
Adding, subtracting and multiplying polynomials are, basically, the same as adding, subtracting and multiplying numbers. They only difference is that we have a pesky variable to worry about, but this video will show you that's no problem, so no worries! This method has worked for many of my students, and I think it will work for you, too!
5. How to Divide Polynomials with Long Division
Arithmetic long division and polynomial long division are very similar. Yes, it's a long process, but once you have the rhythm you will get every problem correct!
6. How to Use Synthetic Division to Divide Polynomials
Synthetic division is a 'short-cut' way of dividing a polynomial by a monomial. You still need to know long division, sorry, but this method is way fun when you're dividing by a monomial!
7. Dividing Polynomials with Long and Synthetic Division: Practice Problems
Let's look at some more polynomial division problems. We will use long division and synthetic division, but this time we will have a couple of more involved problems. So, get out some paper and a pencil and let's begin!
8. Functions: Identification, Notation & Practice Problems
A function is simply a rule that takes one number and turns it into another. But some special conditions must apply for it to be a true mathematical function. Learn about those conditions and how we write functions here!
9. How to Add, Subtract, Multiply and Divide Functions
Adding, subtracting, multiplying and dividing functions is about as simple as substituting in expressions and then just doing whichever operation it asks you to do. Check out this video lesson to see some examples of this and learn just how easy it is!
10. How to Compose Functions
Function composition is the process of putting two or more functions together. This video lesson will explain how this process works and also show you how to evaluate functions that have been composed.
11. Inverse Functions
Inverse functions are two functions that do exactly opposite things. Check out this lesson to learn about how to write inverse functions, find inverse functions, and predict whether or not they exist.
12. How to Multiply and Divide Rational Expressions
Multiplying and dividing rational polynomial expressions is exactly like multiplying and dividing fractions. Like fractions, we will reduce. With polynomial expressions we use factoring and canceling. I also give you a little mnemonic to help you remember when you need a common denominator and when you don't.
13. How to Add and Subtract Rational Expressions
Adding and subtracting rational expressions brings everything you learned about fractions into the world of algebra. We will mix common denominators with factoring and FOILing.
14. How to Solve a Rational Equation
A rational equation is one that contains fractions. Yes, we will be finding a common denominator that has 'x's. But no worries! Together we will use a process that will help us solve rational equations every time!
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Other chapters within the AFOQT: Practice & Study Guide course
- AFOQT: Word Comprehension
- AFOQT: Analogies
- AFOQT: Arithmetic Comprehension
- AFOQT: Arithmetic Equations
- AFOQT: Factoring
- AFOQT: Exponents & Roots
- AFOQT: Word Problems
- AFOQT: Algebraic Expressions
- AFOQT: Graphs, Linear Equations & Parabolas
- AFOQT: Quadratic Equations
- AFOQT: Principles of Geometry
- AFOQT: Lines & Angles
- AFOQT: Circles & Triangles
- AFOQT: Rectangles & Solids
- AFOQT: Figures & Polygons
- AFOQT: Three-dimensional Blocks
- AFOQT: Object Visualization & Manipulation
- AFOQT: Table Knowledge
- AFOQT: Instrument Knowledge
- AFOQT: Aviation
- AFOQT: The Metric System & Scientific Notation
- AFOQT: Atoms & Matter
- AFOQT: Thermodynamics & Electricity
- AFOQT: Magnetism
- AFOQT: Earth Science
- AFOQT: Biomolecules & Cells
- AFOQT: Human Anatomy
- AFOQT: Personality Traits & Attitudes
- AFOQT Flashcards