About This Chapter
Algebra: Polynomials - Chapter Summary
Lessons in this chapter show you that working with variables doesn't have to be difficult. You can practice various ways to multiply binomials, including the FOIL, claw & face and area methods. Professional instructors show you that factoring is actually the FOIL method performed backwards, and they give you plenty of examples to test your competency in this area.
As you work your way through this chapter, you can find out that synthetic division is really just a quick way to divide polynomials by monomials. You can also learn how to solve quadratic equations by factoring, and determine how to complete the square to find the spot where the maximum or minimum parabola lies. Some of the key topics included in this chapter are listed below:
- Adding, subtracting and multiplying polynomials
- Using FOIL (firsts, outsides, insides, lasts) and the area method to multiply binomials
- Solving quadratic equations
- Dividing polynomials with long division and with synthetic division
- Completing the square
- Solving equations with the quadratic formula
This chapter provides ample practice problems with accompanying detailed solutions. The lessons are available in both video and written transcript formats. By taking the quiz at the end of each lesson, you can track your progress and discover any topics that might need more attention. Watch the videos as many times as you like, or use the video tags to get quick access to specific parts of a video lesson. In addition, there are links to text lessons that will explain related key concepts and terms.
1. What are Polynomials, Binomials, and Quadratics?
What do polynomials, binomials, and quadratics have in common? What are their differences? How can you identify each of them? Watch this video lesson to find the answers.
2. 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!
3. Multiplying Binomials Using FOIL and the Area Method
From the distributive property, to FOIL, to the area model, to happy faces and claws, there are many different ways to learn how to multiply binomials. In this lesson, you'll learn how to use all of them and get to pick which one you like the most.
4. Multiplying Binomials Using FOIL & the Area Method: Practice Problems
There are a few mistakes that are easy to make when multiplying binomials with FOIL and also a few ways to complicate problems like this, so why not make sure you're brushed up on your skills? You'll also learn a shortcut and how to use the area method to multiply even bigger polynomials.
5. How to Factor Quadratic Equations: FOIL in Reverse
So, you know how to multiply binomials with the FOIL method, but can you do it backwards? That's exactly what factoring is, and it can be pretty tricky. Check out this lesson to learn a method that will allow you to factor quadratic trinomials with a leading coefficient of 1.
6. Factoring Quadratic Equations: Polynomial Problems with a Non-1 Leading Coefficient
Once you get good at factoring quadratics with 1x squared in the front of the expression, it's time to try ones with numbers other than 1. It will be the same general idea, but there are a few extra steps to learn. Do that here!
7. 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!
8. 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!
9. 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!
10. How to Solve a Quadratic Equation by Factoring
If your favorite video game, 'Furious Fowls,' gave you the quadratic equation for each shot you made, would you be able to solve the equation to make sure every one hit its target? If not, you will after watching this video!
11. How to Solve Quadratics That Are Not in Standard Form
It isn't always the case that your equation will be set up nicely for you to solve. In this lesson, learn how to factor or use the quadratic formula to solve quadratic equations, even when they are not in standard form.
12. How to Complete the Square
Completing the square can help you learn where the maximum or minimum of a parabola is. If you're running a business and trying to make some money, it might be a good idea to know how to do this! Find out what I'm talking about here.
13. Completing the Square Practice Problems
Completing the square is one of the most confusing things you'll be asked to do in an algebra class. Once you get the general idea, it's best to get in there and actually do a few practice problems to make sure you understand the process. Do that here!
14. How to Use the Quadratic Formula to Solve a Quadratic Equation
When solving a quadratic equation by factoring doesn't work, the quadratic formula is here to save the day. Learn what it is and how to use it in this lesson.
15. Using the Quadratic Formula to Solve Equations with Literal Coefficients
Watch this video lesson to find out what steps you need to take to solve equations with literal coefficients using the quadratic formula. Learn why it might be easier to work with literal coefficients than with number coefficients.
16. Solving Problems using the Quadratic Formula
The quadratic formula is not as complicated as it may look. You can learn to tackle this formula and succeed in using it to help you solve your quadratic problems. Watch this video to see how.
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Other chapters within the SAT Subject Test Mathematics Level 1: Practice and Study Guide course
- Basic Arithmetic Calculations
- Rational Numbers
- Square Roots
- Decimals and Percents
- Basic Algebraic Expressions
- Algebraic Linear Equations & Inequalities
- Algebra: Absolute Value Equations & Inequalities
- Understanding the Basics of Functions
- Algebra: Rational Expressions
- Mathematical Sequences
- Understanding Exponentials & Logarithms
- Complex and Imaginary Numbers
- Coordinate Geometry - Graphing
- Lines and Angles
- Properties of Triangles
- Properties of Circles
- Finding Perimeter, Area & Volume
- Solid Geometry
- Trigonometry Basics
- Understanding Probability & Statistics
- SAT Subject Test Mathematics Level 1 Flashcards