Algebra I E-Book

Mary Jane Sterling

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch
• Veröffentlichungsjahr: 2013

Seitenzahl: 393

Beschreibung

1,001 Algebra I Practice Problems For Dummies Practice makes perfect--and helps deepen your understanding of algebra by solving problems 1,001 Algebra I Practice Problems For Dummies, with free access to online practice problems, takes you beyond the instruction and guidance offered in Algebra I For Dummies, giving you 1,001 opportunities to practice solving problems from the major topics in algebra. You start with some basic operations, move on to algebraic properties, polynomials, and quadratic equations, and finish up with graphing. Every practice question includes not only a solution but a step-by-step explanation. From the book, go online and find: * One year free subscription to all 1,001 practice problems * On-the-go access any way you want it--from your computer, smart phone, or tablet * Multiple choice questions on all you math course topics * Personalized reports that track your progress and help show you where you need to study the most * Customized practice sets for self-directed study * Practice problems categorized as easy, medium, or hard Whether you're studying algebra at the high school or college level, the practice problems in 1,001 Algebra I Practice Problems For Dummies give you a chance to practice and reinforce the skill s you learn in the classroom and help you refine your understanding of algebra. Note to readers: 1,001 Algebra I Practice Problems For Dummies, which only includes problems to solve, is a great companion to Algebra I For Dummies, 2nd Edition which offers complete instruction on all topics in a typical Algebra I course.

Leseprobe

1,001 Algebra I Practice Problems For Dummies®

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ISBN 978-1-118-44671-3 (pbk); ISBN 978-1-118-44665-2 (ebk); ISBN 978-1-118-44666-9 (ebk); ISBN 978-1-118-44669-0 (ebk)

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About the Author

Mary Jane Sterling is the author of six For Dummies titles: Algebra I For Dummies, Algebra II For Dummies, Trigonometry For Dummies, Math Word Problems For Dummies, Business Math For Dummies, and Linear Algebra For Dummies. She has also written many supplementary workbooks and study aids.

Mary Jane continues doing what she loves best: teaching mathematics. When not teaching or writing For Dummies books, she loves spending her time reading murder mysteries and fishing for her dinner.

Dedication

The author dedicates this book to her son, Sgt. James T. Sterling, USMC, and the other members of the 4th Air/Naval Gunfire Liaison Company, Det Juliet (part of Operation Enduring Freedom 2012). Jim and the others in his unit, as well as all military serving the U.S., have our utmost respect and appreciation.

Author’s Acknowledgments

The author issues a big thank you to project editor Tim Gallan, who has taken on the huge challenge of creating this new product. He has taken a lot of raw material and made it into this wonderful, finished workbook. Thank you so much for your hard work and patience.

Also, a heartfelt thank you to the math editors, Suzanne Langebartels and Stephanie Long. As careful as I may be to do all the problems correctly, there is always that chance of a silly error. The editors keep me honest!

And, of course, a grateful thank you to acquisitions editor Lindsay Lefevere, who again found me another interesting project.

Publisher’s Acknowledgments

We’re proud of this book; please send us your comments at http://dummies.custhelp.com. For other comments, please contact our Customer Care Department within the U.S. at 877-762-2974, outside the U.S. at 317-572-3993, or fax [phone].

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1,001 Algebra I Practice Problems For Dummies®

Visit www.dummies.com/cheatsheet/1001Algebra1 to view this book's cheat sheet.

Table of Contents

Introduction

What You’ll Find

How This Workbook Is Organized

Part I: Questions

Part II: Answers

Beyond the Book

What you’ll find online

How to register

Where to Go for Additional Help

Part I: The Questions

Chapter 1: Signing on with Signed Numbers

The Problems You’ll Work On

What to Watch Out For

Chapter 2: Recognizing Algebraic Properties and Notation

The Problems You’ll Work On

What to Watch Out For

Chapter 3: Working with Fractions and Decimals

The Problems You’ll Work On

What to Watch Out For

Chapter 4: Making Exponential Expressions and Operations More Compatible

The Problems You’ll Work On

What to Watch Out For

Chapter 5: Raking in Radicals

The Problems You’ll Work On

What to Watch Out For

Chapter 6: Creating More User-Friendly Algebraic Expressions

The Problems You’ll Work On

What to Watch Out For

Chapter 7: Multiplying by One or More Terms

The Problems You’ll Work On

What to Watch Out For

Chapter 8: Dividing Algebraic Expressions

The Problems You’ll Work On

What to Watch Out For

Chapter 9: Factoring Basics

The Problems You’ll Work On

What to Watch Out For

Chapter 10: Factoring Binomials

The Problems You’ll Work On

What to Watch Out For

Chapter 11: Factoring Quadratic Trinomials

The Problems You’ll Work On

What to Watch Out For

Chapter 12: Other Factoring Techniques

The Problems You’ll Work On

What to Watch Out For

Chapter 13: Solving Linear Equations

The Problems You’ll Work On

What to Watch Out For

Chapter 14: Taking on Quadratic Equations

The Problems You’ll Work On

What to Watch Out For

Chapter 15: Solving Polynomials with Powers Three and Higher

The Problems You’ll Work On

What to Watch Out For

Chapter 16: Reining in Radical and Absolute Value Equations

The Problems You’ll Work On

What to Watch Out For

Chapter 17: Making Inequalities More Fair

The Problems You’ll Work On

What to Watch Out For

Chapter 18: Using Established Formulas

The Problems You’ll Work On

What to Watch Out For

Chapter 19: Using Formulas in Geometric Story Problems

The Problems You’ll Work On

What to Watch Out For

Chapter 20: Tackling Traditional Story Problems

The Problems You’ll Work On

What to Watch Out For

Chapter 21: Graphing Basics

The Problems You’ll Work On

What to Watch Out For

Chapter 22: Using the Algebra of Lines

The Problems You’ll Work On

What to Watch Out For

Chapter 23: Other Graphing Topics

The Problems You’ll Work On

What to Watch Out For

Part II: The Answers

Chapter 24: Answers

Answers 1 - 100

Answers 101 - 200

Answers 201 - 300

Answers 301 - 400

Answers 401 - 500

Answers 501 - 600

Answers 601 - 700

Answers 701 - 800

Answers 801 - 900

Answers 901 - 1001

Cheat Sheet

Introduction

One-thousand-one algebra problems: That’s a lot of algebra problems.

It will take you seven days to do all of them, if you do 143 each day. Whew! It will take you 91 days to do all of them, if you manage to do 11 each day. And, of course, it will take you 1,001 days to do all the problems if you do just one each day. Whatever your game plan, this is still a lot of problems. You may want to start at the beginning and do each problem in turn, or you may want to jump around and do the problems in an order that suits you best. Either plan is doable. Either plan is fine. Just watch out for topics that build on one another — you may need the information from one skill to succeed in another.

Practice makes perfect. Unlike other subjects where you can just read or listen and absorb the information sufficiently, mathematics takes practice. The only way to figure out how the different algebraic rules work and interact with one another is to get into the problems — get your hands dirty, so to speak. Many problems appear to be the same, on the surface, but different aspects and challenges have been inserted to make the different problems unique. The concepts become more set in your mind when you work with the problems and have the properties confirmed with your solutions.

Yes, one-thousand-one algebra problems are a lot of problems. But you may find that this just whets your appetite for more. Enjoy!

What You’ll Find

This book has 1,001 algebra problems divided up among 23 chapters. Each chapter has many different sets of questions. The sets of questions are sometimes in a logical, sequential order, going from one part of a topic to the next and then to the next. Other times the sets of questions represent the different ways a topic can be presented. In any case, you’re given instructions on doing the problems. And sometimes you’re given a particular formula or format to use.

Instead of just having answers to each of the problems, you find a worked-out solution for each and every one. Flip to the back of the book for the step-by-step process needed to solve the problems. The solutions include verbal explanations inserted in the work where necessary. Sometimes an alternate procedure may be offered. Not everyone does algebra exactly the same way, but this book tries to provide the most understandable and success-promoting process to use when solving the algebra problems presented.

How This Workbook Is Organized

This workbook is divided into two main parts: questions and answers. But you probably figured that out already.

Part I: Questions

The questions chapters cover many different topics:

Basic operations: The first six chapters cover the types of numbers and the types of operations on those numbers that are essential to working in algebra. The natural numbers and whole numbers are fine for elementary arithmetic, but you need to broaden your horizons with signed numbers and decimals and fractions and exponential expressions. All these types of numbers are added, subtracted, multiplied, and divided. The rules for the different types of numbers have similarities and differences. The problems can help you come to grips with these situations and recognize what’s the same and what’s different.

Also important in algebra are the operations involving radicals, absolute value, and factorial. And, tying together all the numbers and operations are the rules on how to deal with them: the order in which you perform the operations, and then the effect of grouping symbols on the whole process.

Algebraic expressions: An algebraic expression can consist of one or more terms — separated by addition and subtraction — or it can be in factored form. The factored form has everything connected by multiplication and division. Each of these forms is useful in some process or another, so it’s important to be able to change from one form to another and back again. Multiply out the factors if you want a listing of terms from highest exponent to lowest. Or, factor many terms to make them all just one if you want to solve for a root or reduce some fraction.

You’ll find techniques for multiplying by one term or two — or more. There are some helpful tricks for raising binomials to higher powers. And then you find the factoring techniques — from rules of divisibility to factoring by grouping. One of the challenges of factoring expressions is deciding which technique to use. You find lots of practice to help you make those decisions.

Solving equations: What is the point of learning all those algebra basics and then going through the factoring process? One of the favorite and most common goals for all that practice is to use the techniques to solve an equation. Solving an equation means identifying the number or numbers you can replace the variable with to make a true statement.

You’ll find factoring and the multiplication property of zero to be your first approach, and then you’ll also have the quadratic formula to use on some of the more challenging second-degree equations. Polynomials can be solved using synthetic division to help with the factoring. And then you have radical and absolute value equations — with their particular challenges. Finish the section off with inequalities, and you’ll have run the gamut of solving for what variables can represent.

Applications: Mention the words story problem, and you’ll see either a shudder or a brightening smile. People either love them or they don’t. But story problems (practical applications) are a main goal of learning to use algebra effectively.

The practical applications found in this section of the workbook are broken into many different types. You find some that are based on an established formula: area, perimeter, simple interest, and so on. Other applications have to do with relationships between numbers or sizes of objects. The trick to doing those applications is understanding the wording, which is why you come armed with all the basics under your belt. Get to work on the work problems before you age too much with the age problems. Just write yourself a simple algebraic equation, and you’re almost finished.

Graphing: Most of us are very visual — we understand things better when a picture is drawn. I usually draw pictures when working on word problems; it helps me focus on what type of equation to write. But the pictures in this section are a bit more structured. The pictures here involve the Cartesiancoordinate system, which involves placing points, segments, and lines in their proper positions. Graphing lines is often used when solving systems of equations. And graphing is found in pretty much all the mathematics that follows algebra. This is where you can get a good start on the topic.

Part II: Answers

This part provides not only the answers to all the questions but explanations of the answers as well. So you get the solution, and you see how to arrive at that solution.

Beyond the Book

This book is chock-full of algebra goodness — I’ve given you enough problems to significantly improve your confidence with all things algebra. But maybe you want to track your progress as you tackle the problems, or maybe you’re stuck on a few types of algebra problems and wish they were all presented in one place where you could methodically make your way through them. No problem! Your book purchase comes with a free one-year subscription to all 1,001 practice problems online. You get on-the-go access any way you want it — from your computer, smartphone, or tablet. Track your progress and view personalized reports that show where you need to study the most. And then do it. Study what, where, when, and how you want.

What you’ll find online

The online practice that comes free with this book offers you the same 1,001 questions and answers that are available here, presented in a multiple-choice format. The beauty of the online problems is that you can customize your online practice to focus on the topic areas that give you the most trouble. So if you aren’t yet a whiz at factoring polynomials and solving quadratic equations, then select these problem types and BAM! — just those types of problems appear for your solving pleasure. Or, if you’re short on time but want to get a mixed bag of a limited number of problems, you can plug in the quantity of problems you want to practice and that many — or few — of a variety of algebra problems appears. Whether you practice a couple hundred problems in one sitting or a couple dozen, and whether you focus on a few types of problems or practice every type, the online program keeps track of the questions you get right and wrong so that you can monitor your progress and spend time studying exactly what you need.

You can access this online tool using a PIN code, as described in the next section. Keep in mind that you can create only one login with your PIN. Once the PIN is used, it’s no longer valid and is nontransferable. So you can’t share your PIN with other users after you’ve established your login credentials.

How to register

Purchasing this book entitles you to one year of free access to the online, multiple-choice version of all 1,001 of this book’s practice problems. All you have to do is register. Just follow these simple steps:

1. Find your PIN code.

• Print book users: If you purchased a hard copy of this book, turn to the back of this book to find your PIN.

• E-book users: If you purchased this book as an e-book, you can get your PIN by registering your e-book at dummies.com/go/getaccess. Go to this website, find your book and click it, and then answer the security question to verify your purchase. Then you'll receive an e-mail with your PIN.

2. Go to onlinepractice.dummies.com.

3. Enter your PIN.

4. Follow the instructions to create an account and establish your own login information.

That’s all there is to it! You can come back to the online program again and again — simply log in with the username and password you choose during your initial login. No need to use the PIN a second time.

If you have trouble with the PIN or can't find it, please contact Wiley Product Technical Support at 800-762-2974 or http://support.wiley.com.

Your registration is good for one year from the day you activate your PIN. After that time frame has passed, you can renew your registration for a fee. The website gives you all the important details about how to do so.

Where to Go for Additional Help

The written directions given with the individual problems are designed to tell you what you need to do to get the correct answer. Sometimes the directions may seem vague if you aren’t familiar with the words or the context of the words. Go ahead and look at the solution to see if that helps you with the meaning. But if the vocabulary is still unrecognizable, you may want to refer to the glossary in an algebra book, such as Algebra I For Dummies, written by yours truly and published by the fine folks at Wiley.

The solution to each problem is given at the end of its respective chapter. But you may not be able to follow from one step to the next. Is something missing? This book is designed to provide you with enough practice to become very efficient in algebra, but it isn’t intended to give the step-by-step explanation on how and why each step is necessary. You may need to refer to Algebra I For Dummies or Algebra I Essentials For Dummies (also written by me and published by Wiley) to get more background on a problem or to understand why a particular step is taken in the solution of the problem.

Part I

The Questions

Visit www.dummies.com for great Dummies content online

In this part . . .

One thousand and one algebra problems. That’s a lot of work. But imagine how much work it was for me to write them. Don’t get me started. Anyway, here are the general types of questions you’ll be dealing with:

Performing basic operations (Chapters 1 through 6)

Changing the format of algebraic expressions (Chapters 7 through 12)

Solving Equations (Chapters 13 through 17)

Applying algebra by using formulas and solving word problems (Chapters 18 through 20)

Graphing (Chapters 21 through 23)

Chapter 1

Signing on with Signed Numbers

Signed numbers include all real numbers, positive or negative, except 0. In other words, signed numbers are all numbers that have a positive or negative sign. You usually don’t put a plus sign in front of a positive number, though, unless you’re doing math problems. When you see the number 7, you just assume that it’s +7. The number 0 is the only number that isn’t either positive or negative and doesn’t have a plus or minus sign in front of it; it’s the dividing place between positive and negative numbers.

The Problems You’ll Work On

As you work with signed numbers (and positive and negative values), here are the types of problems you’ll do in this chapter:

Placing numbers in their correct position on the number line — starting from smallest to largest as you move from left to right

Performing the absolute value operation — determining the distance from the number to 0

Adding signed numbers — finding the sum when the signs are the same, and finding the difference when the signs are different

Subtracting signed numbers — changing the second number to its opposite and then using the rules for addition

Multiplying and dividing signed numbers — counting the number of negative signs and assigning a positive sign to the answer when an even number of negatives exist and a negative sign to the answer when an odd number of negatives exist

What to Watch Out For

Pay careful attention to the following items when working on the signed number problems in this chapter:

Keeping track of the order of numbers when dealing with negative numbers and fractions

Working from left to right when adding and subtracting more than two terms

Determining the sign when multiplying and dividing signed numbers, being careful not to include numbers without signs when counting how many negatives are present

Reducing fractions correctly and dividing only by common factors

Placing Real Numbers on the Number Line

1–6 Determine the correct order of the numbers on the real number line.

1. Determine the order of the numbers:

–3, 4, –1, 0, –4

2. Determine the order of the numbers:

–3, 3, –2, 0, 1

3. Determine the order of the numbers:

4. Determine the order of the numbers:

5. Determine the order of the numbers:

6. Determine the order of the numbers:

Using the Absolute Value Operation

7–10 Evaluate each expression involving absolute value.

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8.

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Adding Signed Numbers

11–20 Find the sum of the signed numbers.

Subtracting Signed Numbers

21–30 Find the difference between the signed numbers.

Multiplying and Dividing Signed Numbers

31 – 50 Find the products and quotients involving signed numbers.

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Chapter 4

Making Exponential Expressions and Operations More Compatible

An exponential expression consists of a base and a power. The general format of an exponential expression is bn, where b is the base and n is the power or exponent. The base, b, has to be a positive number, and the power, n, is a real number. Positive powers, negative powers, and fractional powers all have special meanings and designations.

The Problems You’ll Work On

Here are some of the things you do in this chapter:

Multiplying and dividing exponential factors with the same base

Raising a power to a power — putting an exponent on an exponential expression

Combining operations— deciding what comes first when multiplying, dividing, and raising to powers

Changing numbers to the same base so they can be combined

Writing numbers using scientific notation

What to Watch Out For

Be sure you also remember the following:

Writing fractional expressions by using the correct power of a base

Recognizing a common base in different numbers

Remembering when to add, subtract, and multiply the exponents

Using the correct power of ten in scientific notation expressions

Multiplying and Dividing Exponentials with the Same Base

141–150 Perform the operations and simplify.

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Raising a Power to a Power

151–160 Compute the powers and simplify your answers.

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Combining Different Operations on Exponentials

161–170 Use the order of operations to compute the final answers.

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Changing the Base to Perform an Operation

171–180 Perform the operations by changing the numbers to the same base.

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Working with Scientific Notation

181–190 Perform the operations on the numbers written in scientific notation. Write your answer in scientific notation.

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Chapter 5

Raking in Radicals

Radical expressions are characterized by radical symbols and an index — a small number written in front of the radical symbol that indicates whether you have a cube root, a fourth root, and so on. When no number is written in front of the radical, you assume it’s a square root.

The Problems You’ll Work On

In this chapter, you get plenty of practice working with radicals in the following ways:

Simplifying radical expressions by finding a perfect square factor

Rationalizing denominators with one term

Rationalizing denominators with two terms, using a conjugate

Rewriting radicals with fractional exponents

Dividing with radicals

Solving operations involving fractional exponents

Estimating the values of radical expressions

What to Watch Out For

As you get in your groove, solving one radical problem after another, don’t overlook the following:

Choosing the largest perfect square factor when simplifying a radical expression

Multiplying correctly when writing equivalent fractions, using conjugates

Performing operations correctly when fractions are involved

Checking radical value estimates by comparing to nearest perfect square values

Simplifying Radical Expressions

191–196 Simplify the radical expressions.

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Rationalizing Denominators

197–210 Simplify the fractions by rationalizing the denominators.

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Using Fractional Exponents for Radicals

211–216 Rewrite each radical expression using a fractional exponent.

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Evaluating Expressions with Fractional Exponents

217–226 Compute the value of each expression.

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Operating on Radicals

227–234 Perform the operations on the radicals.

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Operating on Factors with Fractional Exponents

235–242 Perform the operations on the expressions.

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Estimating Values of Radicals

243–250 Estimate the value of the radicals to the nearer tenth after simplifying the radicals. Use:

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Chapter 7

Multiplying by One or More Terms

Multiplying algebraic expressions is much like multiplying numbers, but the introduction of variables makes the process just a bit more interesting. Products involving variables call on the rules of exponents. And, because of the commutative property of addition and multiplication, arrangements and rearrangements of terms and factors can make the process simpler.

The Problems You’ll Work On

When multiplying by one or more terms, you deal with the following in this chapter:

Distributing terms with one or more factors over two or more terms — multiplication over sums and differences

Distributing division over sums and differences and dividing each term in the parentheses

Distributing binomials over binomials or trinomials and then combining like terms

Multiplying binomials using FOIL: First, Outer, Inner, Last

Using Pascal’s triangle to find powers of binomials

Finding products of binomials times trinomials that create sums and differences of cubes

What to Watch Out For

With all the distributing and multiplying, don’t overlook the following:

Applying the rules of exponents to all terms when distributing variables over several terms

Changing the sign of each term when distributing a negative factor over several terms

Combining the outer and inner terms correctly when applying FOIL

Starting with the zero power when assigning powers of the second term to the pattern in Pascal’s triangle

Distributing One Term Over Sums and Differences

311–315 Distribute the number over the terms in the parentheses.

311. 3(2x + 4)

312. –4(5y – 6)

313. 7(x2 – 2x + 3)

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315.

Distributing Using Division

316–320 Perform the division by dividing each term in the numerator by the term in the denominator.

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Multiplying Binomials Using Distributing

321–325 Distribute the first binomial over the second binomial and simplify.

321. (a + 1)(x – 2)

322. (y – 4)(z2 + 7)

323. (x + 2)(y – 2)

324. (x2 – 7)(x3 – 8)

325. (x2 + y4)(x2 – y4)

Multiplying Binomials Using FOIL

326–335 Multiply the binomials using “FOIL.”

326. (x – 3)(x + 2)

327. (y + 6)(y + 4)

328. (2x – 3)(3x – 2)

329. (z – 4)(3z – 8)

330. (5x + 3)(4x – 2)

331. (3y – 4)(7y + 4)

332. (x2 – 1)(x2 + 1)

333. (2y3 + 1)(3y3 – 2)

334. (8x – 7)(8x + 7)

335. (2z2 + 3)(2z2 – 3)

Distributing Binomials Over Trinomials

336–340 Distribute the binomial over the trinomial and simplify.

336. (x + 3)(x2 – 2x + 1)

337. (y – 2)(y2 + 3y + 4)

338. (2z + 1)(z2 + z + 7)

339. (4x – 3)(2x2 + 2x + 1)

340. (y + 7)(3y2 – 7y + 5)

Squaring Binomials

341–345 Square the binomials.

341. (x + 5)2

342. (y – 6)2

343. (4z + 3)2

344. (5x – 2)2

345. (8x + y)2

Raising Binomials to the Third Power

346–350 Raise the binomials to the third power.

346. (x + 2)3

347. (y – 4)3

348. (3z + 2)3

349. (2x2 + 1)3

350. (a2 – b)3

Using Pascal’s Triangle

351–360 Raise the binomial to the indicated power.

351. (x + 3)4

352. (y – 2)5

353. (z + 1)6

354. (a + b)7

355. (x – 2)7

356. (4z + 1)4

357. (3y – 2)5

358. (2x + 3)6

359. (3x + 2y)4

360. (2z – 3w)5

Finding Special Products of Binomials and Trinomials

361–365 Distribute the binomial over the trinomial to determine the “special” product.

361. (x – 1)(x2 + x + 1)

362. (y + 2)(y2 – 2y + 4)

363. (z – 4)(z2 + 4z + 16)

364. (3x – 2)(9x2 + 6x + 4)

365. (5z + 2w)(25z2 – 10zw + 4w2)

Chapter 8

Dividing Algebraic Expressions

Division is the opposite or inverse of multiplication. Instead of adding exponents, you subtract the exponents of like variables. When dividing an expression containing several terms by an expression containing just one term, you have two possible situations: the divisor evenly divides each term, meaning fractions formed from each term and the divisor reduce to denominators of 1, or the divisor doesn’t evenly divide one or more of the terms. What you do with the second situation depends on the application you’re working on at the time. The problems in this chapter present various options.

The Problems You’ll Work On

The problems in this chapter are all about division and include the following:

Dividing several terms by a number

Dividing several terms by a term containing numerical and variable factors

Dividing several terms by a binomial, using long division

Dividing several terms by a binomial, using synthetic division

Dividing by trinomials

What to Watch Out For

As you work through dividing one expression after another, watch out for the following:

Assigning the correct sign to each term in the result

Remembering to change the sign of each term when dividing by a negative term

Changing the signs of all products of quotient term times divisor term in each step of a long division problem

Inserting zeros for missing terms when using synthetic division

Changing the sign of the number in the binomial when setting up a synthetic division problem

Starting with an exponent one smaller than that in the divisor when writing the quotient in a synthetic division problem

Dividing with Monomial Divisors

366–375 Divide each numerator by the monomial.

366.

367.

368.

369.

370.

371.

372.

373.

374.

375.

Monomial Divisors and Remainders

376–385 Divide each numerator by the monomial. Write any remainders as fractions.

376.

377.

378.

379.

380.

381.

382.

383.

384.

385.

Using Long Division to Divide with Binomials

386–395 Divide each numerator by the binomial, using long division. Write any remainders as fractions.

386.

387.

388.

389.

390.

391.

392.

393.

394.

395.

Dividing with Binomials Using Synthetic Division

396–405 Divide each numerator by the binomial, using synthetic division. Write any remainders as fractions.

396.

397.

398.

399.

400.

401.

402.

403.

404.

405.

Dividing with Higher Power Divisors

406–415 Divide each numerator by the denominator, using long division. Write any remainders as fractions.

406.

407.

408.

409.

410.

411.

412.

413.

414.

415.