Algebra II For Dummies. Sterling Mary Jane

and separated from other constants and variables by addition or subtraction.

      ✔ trinomial: An expression with three terms.

      ✔ variable: Something that can have many values (usually represented by a letter to indicate that you have many choices for its value).

      If you feel a bit over your head after reading through some chapters, you may want to refer to Algebra For Dummies (Wiley) for a more complete explanation of the basics. My feelings won’t be hurt; I wrote that one, too!

      Icons Used in This Book

      The icons that appear in this book are great for calling attention to what you need to remember or what you need to avoid when doing algebra. Think of the icons as signs along the Algebra II Highway; you pay attention to signs – you don’t run them over!

      

This icon provides you with the rules of the road. You can’t go anywhere without road signs – and in algebra, you can’t get anywhere without following the rules that govern how you deal with operations. In place of “Don’t cross the solid yellow line,” you see “Reverse the sign when multiplying by a negative.” Not following the rules gets you into all sorts of predicaments with the Algebra Police (namely, your instructor).

      

This icon is like the sign alerting you to the presence of a sports arena, museum, or historical marker. Use this information to improve your mind, and put the information to work to improve your algebra problem-solving skills.

      

This icon lets you know when you’ve come to a point in the road where you should soak in the information before you proceed. Think of it as stopping to watch an informative sunset. Don’t forget that you have another 30 miles to Chicago. Remember to check your answers when working with rational equations.

      

This icon alerts you to common hazards and stumbling blocks that could trip you up – much like “Watch for Falling Rock” or “Railroad Crossing.” Those who have gone before you have found that these items can cause a huge failure in the future if you aren’t careful.

      

Yes, Algebra II does present some technical items that you may be interested to know. Think of the temperature or odometer gauges on your dashboard. The information they present is helpful, but you can drive without it, so you can simply glance at it and move on if everything is in order.

      Beyond the Book

      In addition to all the great content provided in this book, you can find even more of it online. Check out www.dummies.com/cheatsheet/algebraii for a free Cheat Sheet that provides you with a quick reference to some standard forms, such as special products and equations of conics; some formulas, such as those needed for counting techniques and sequences and series; and, yes, those ever-important laws of logarithms.

      You can also find several bonus articles on topics such as just what a normal line is (as opposed to abnormal?) and how mathematics helped a young man become king at www.dummies.com/extras/algebraii.

      Where to Go from Here

      I’m so pleased that you’re willing, able, and ready to begin an investigation of Algebra II. If you’re so pumped up that you want to tackle the material cover to cover, great! But you don’t have to read the material from page one to page two and so on. You can go straight to the topic or topics you want or need and refer to earlier material if necessary. You can also jump ahead if so inclined. I include clear cross-references in chapters that point you to the chapter or section where you can find a particular topic – especially if it’s something you need for the material you’re looking at or if it extends or furthers the discussion at hand.

      You can use the table of contents at the beginning of the book and the index in the back to navigate your way to the topic that you need to brush up on. Or, if you’re more of a freewheeling type of guy or gal, take your finger, flip open the book, and mark a spot. No matter your motivation or what technique you use to jump into the book, you won’t get lost because you can go in any direction from there.

      Enjoy!

      Part I

      Homing in on Basic Solutions

      

For Dummies has great info on lots of different topics. Check out www.dummies.com to find out how you and learn more and do more with For Dummies.

       In this part …

      ✔ Get a handle on the basics of simplifying and factoring.

      ✔ Find out how to get in line with linear equations.

      ✔ Queue up to quadratic equations.

      ✔ Take on basic rational and radical equations.

      ✔ Work through graphing on the coordinate system.

      Chapter 1

      Going Beyond Beginning Algebra

       In This Chapter

      ▶ Abiding by (and using) the rules of algebra

      ▶ Adding the multiplication property of zero to your repertoire

      ▶ Raising your exponential power

      ▶ Looking at special products and factoring

      Algebra is a branch of mathematics that people study before they move on to other areas or branches in mathematics and science. For example, you use the processes and mechanics of algebra in calculus to complete the study of change; you use algebra in probability and statistics to study averages and expectations; and you use algebra in chemistry to work out the balance between chemicals. Algebra all by itself is esthetically pleasing, but it springs to life when used in other applications.

      Any study of science or mathematics involves rules and patterns. You approach the subject with the rules and patterns you already know, and you build on those rules with further study. The reward is all the new horizons that open up to you.

      Any discussion of algebra presumes that you’re using the correct notation and terminology. Algebra I (check out Algebra I For Dummies [Wiley]) begins with combining terms correctly, performing operations on signed numbers, and dealing with exponents in an orderly fashion. You also solve the basic types of linear and quadratic equations. Algebra II gets into more types of functions, such as exponential and logarithmic functions, and topics that serve as launching spots for other math courses.

      Going into a bit more detail, the basics of algebra include rules for dealing with equations, rules for using and combining terms with exponents, patterns to use when factoring expressions, and a general order for combining all the above. In this chapter, I present these basics so you can further your study of algebra and feel confident in your algebraic ability. Refer to these rules whenever needed as you investigate the many advanced topics in algebra.

      Outlining Algebraic Properties

      Mathematicians developed the rules and properties you use in algebra so that every student, researcher, curious scholar, and bored geek working on the same problem would get the same answer – no matter the time or place. You don’t want the rules changing on you every day (and I don’t want to have to write a new book every year!); you want consistency and security, which you get from the strong algebra rules and properties that I present in this section.

Keeping order with the commutative property