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, TABLE OF CONTENTS
Instructor's Solutions Manual for Algebra: A Combined Approach,
ST
6th Edition
Author: Elayn Martin-Gay
UV
Prealgebra Review
Chapter 1. Real Numbers and Introduction to Algebra
I
Chapter 2. Equations, Inequalities, and Problem Solving
A_
Chapter 3. Graphing Equations and Inequalities
Chapter 4. Systems of Equations
M
Chapter 5. Exponents and Polynomials
Chapter 6. Factoring Polynomials
Chapter 7. Rational Expressions
ED
Chapter 8. Graphs and Functions
Chapter 9. Systems of Equations and Inequalities and Variation
CO
Chapter 10. Rational Exponents, Radicals, and Complex Numbers
Chapter 11. Quadratic Equations and Functions
Chapter 12. Exponential and Logarithmic Functions
NN
Chapter 13. Conic Sections
OI
SS
EU
R?
, Contents
ST
Chapter R 1
UV
Chapter 1 23
Chapter 2 55
I
Chapter 3 118
A_
Chapter 4 171
M
Chapter 5 215
ED
Chapter 6 259
Chapter 7 300
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Chapter 8 355
Chapter 9 388
NN
Chapter 10 429
OI
Chapter 11 477
Chapter 12 583
SS
Chapter 13 642
EU
Appendices 699
Practice Final Exam 724
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, Chapter R
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Section R.1 Practice Exercises 3. A natural number that has exactly two different
factors, 1 and itself, is called a prime number.
1. 10 = 1 ⋅ 10, 10 = 2 ⋅ 5
The factors of 10 are 1, 2, 5, and 10. 4. The least common multiple of a list of numbers
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is the smallest number that is a multiple of all the
2. 18 = 1 ⋅ 18, 18 = 2 ⋅ 9, 18 = 3 ⋅ 6 numbers in the list.
The factors of 18 are 1, 2, 3, 6, 9, and 18.
5. To factor means to write as a product.
3. 5 is a prime number. Its factors are 1 and 5 only.
I
16 is a composite number. Its factors are 1, 2, 4, 6. A multiple of a number is the product of that
8, and 16. number and any natural number.
A_
23 is a prime number. Its factors are 1 and 23
only. 7. No, the natural number 1 is neither prime nor
42 is a composite number. Its factors are 1, 2, 3, composite.
6, 7, 14, 21, and 42.
8. We may write factors in different order, but
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4. 44 = 4 ⋅ 11 = 2 ⋅ 2 ⋅ 11 every natural number has only one prime
The prime factorization of 44 is 2 ⋅ 2 ⋅ 11. factorization.
5. 60 = 4 ⋅ 15 = 2 ⋅ 2 ⋅ 3 ⋅ 5 9. The least common multiple, LCM, of a list of
ED
numbers is the smallest number that is a multiple
The prime factorization of 60 is 2 ⋅ 2 ⋅ 3 ⋅ 5.
of each number in the list.
11
Exercise Set R.1
6. 3 33
CO
3 99 2. 8 = 1 ⋅ 8, 8 = 2 ⋅ 4
The factors of 8 are 1, 2, 4, and 8.
3 297
The prime factorization of 297 is 3 ⋅ 3 ⋅ 3 ⋅ 11. 4. 36 = 1 ⋅ 36, 36 = 2 ⋅ 18, 36 = 3 ⋅ 12, 36 = 4 ⋅ 9,
36 = 6 ⋅ 6
NN
7. 14 = 2 ⋅ 7 The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and
35 = 5 ⋅ 7 36.
LCM = 2 ⋅ 5 ⋅ 7 = 70
6. 63 = 1 ⋅ 63, 63 = 3 ⋅ 21, 63 = 7 ⋅ 9
8. 5 = 5 The factors of 63 are 1, 3, 7, 9, 21, and 63.
9=3⋅3
OI
8. 50 = 1 ⋅ 50, 50 = 2 ⋅ 25, 50 = 5 ⋅ 10
LCM = 3 ⋅ 3 ⋅ 5 = 45
The factors of 50 are 1, 2, 5, 10, 25, and 50.
9. 4 = 2 ⋅ 2
10. 31 = 1 ⋅ 31
15 = 3 ⋅ 5
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The factors of 31 are 1 and 31.
10 = 2 ⋅ 5
LCM = 2 ⋅ 2 ⋅ 3 ⋅ 5 = 60 12. 21 is a composite number. Its factors are 1, 3, 7,
and 21.
Vocabulary, Readiness & Video Check R.1
EU
14. 53 is a prime number. Its factors are only 1 and
1. The number 40 equals 2 ⋅ 2 ⋅ 2 ⋅ 5. Since each 53.
factor is prime, we call 2 ⋅ 2 ⋅ 2 ⋅ 5 the prime
factorization of 40. 16. 51 is a composite number. Its factors are 1, 3, 17,
and 51.
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2. A natural number, other than 1, that is not prime
is called a composite number. 18. 307 is a prime number. Its factors are only 1 and
307.
Copyright © 2020 Pearson Education, Inc. 1
EU
SS
OI
NN
CO
ED
M
IA_
UV
ST
, TABLE OF CONTENTS
Instructor's Solutions Manual for Algebra: A Combined Approach,
ST
6th Edition
Author: Elayn Martin-Gay
UV
Prealgebra Review
Chapter 1. Real Numbers and Introduction to Algebra
I
Chapter 2. Equations, Inequalities, and Problem Solving
A_
Chapter 3. Graphing Equations and Inequalities
Chapter 4. Systems of Equations
M
Chapter 5. Exponents and Polynomials
Chapter 6. Factoring Polynomials
Chapter 7. Rational Expressions
ED
Chapter 8. Graphs and Functions
Chapter 9. Systems of Equations and Inequalities and Variation
CO
Chapter 10. Rational Exponents, Radicals, and Complex Numbers
Chapter 11. Quadratic Equations and Functions
Chapter 12. Exponential and Logarithmic Functions
NN
Chapter 13. Conic Sections
OI
SS
EU
R?
, Contents
ST
Chapter R 1
UV
Chapter 1 23
Chapter 2 55
I
Chapter 3 118
A_
Chapter 4 171
M
Chapter 5 215
ED
Chapter 6 259
Chapter 7 300
CO
Chapter 8 355
Chapter 9 388
NN
Chapter 10 429
OI
Chapter 11 477
Chapter 12 583
SS
Chapter 13 642
EU
Appendices 699
Practice Final Exam 724
R?
, Chapter R
ST
Section R.1 Practice Exercises 3. A natural number that has exactly two different
factors, 1 and itself, is called a prime number.
1. 10 = 1 ⋅ 10, 10 = 2 ⋅ 5
The factors of 10 are 1, 2, 5, and 10. 4. The least common multiple of a list of numbers
UV
is the smallest number that is a multiple of all the
2. 18 = 1 ⋅ 18, 18 = 2 ⋅ 9, 18 = 3 ⋅ 6 numbers in the list.
The factors of 18 are 1, 2, 3, 6, 9, and 18.
5. To factor means to write as a product.
3. 5 is a prime number. Its factors are 1 and 5 only.
I
16 is a composite number. Its factors are 1, 2, 4, 6. A multiple of a number is the product of that
8, and 16. number and any natural number.
A_
23 is a prime number. Its factors are 1 and 23
only. 7. No, the natural number 1 is neither prime nor
42 is a composite number. Its factors are 1, 2, 3, composite.
6, 7, 14, 21, and 42.
8. We may write factors in different order, but
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4. 44 = 4 ⋅ 11 = 2 ⋅ 2 ⋅ 11 every natural number has only one prime
The prime factorization of 44 is 2 ⋅ 2 ⋅ 11. factorization.
5. 60 = 4 ⋅ 15 = 2 ⋅ 2 ⋅ 3 ⋅ 5 9. The least common multiple, LCM, of a list of
ED
numbers is the smallest number that is a multiple
The prime factorization of 60 is 2 ⋅ 2 ⋅ 3 ⋅ 5.
of each number in the list.
11
Exercise Set R.1
6. 3 33
CO
3 99 2. 8 = 1 ⋅ 8, 8 = 2 ⋅ 4
The factors of 8 are 1, 2, 4, and 8.
3 297
The prime factorization of 297 is 3 ⋅ 3 ⋅ 3 ⋅ 11. 4. 36 = 1 ⋅ 36, 36 = 2 ⋅ 18, 36 = 3 ⋅ 12, 36 = 4 ⋅ 9,
36 = 6 ⋅ 6
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7. 14 = 2 ⋅ 7 The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and
35 = 5 ⋅ 7 36.
LCM = 2 ⋅ 5 ⋅ 7 = 70
6. 63 = 1 ⋅ 63, 63 = 3 ⋅ 21, 63 = 7 ⋅ 9
8. 5 = 5 The factors of 63 are 1, 3, 7, 9, 21, and 63.
9=3⋅3
OI
8. 50 = 1 ⋅ 50, 50 = 2 ⋅ 25, 50 = 5 ⋅ 10
LCM = 3 ⋅ 3 ⋅ 5 = 45
The factors of 50 are 1, 2, 5, 10, 25, and 50.
9. 4 = 2 ⋅ 2
10. 31 = 1 ⋅ 31
15 = 3 ⋅ 5
SS
The factors of 31 are 1 and 31.
10 = 2 ⋅ 5
LCM = 2 ⋅ 2 ⋅ 3 ⋅ 5 = 60 12. 21 is a composite number. Its factors are 1, 3, 7,
and 21.
Vocabulary, Readiness & Video Check R.1
EU
14. 53 is a prime number. Its factors are only 1 and
1. The number 40 equals 2 ⋅ 2 ⋅ 2 ⋅ 5. Since each 53.
factor is prime, we call 2 ⋅ 2 ⋅ 2 ⋅ 5 the prime
factorization of 40. 16. 51 is a composite number. Its factors are 1, 3, 17,
and 51.
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2. A natural number, other than 1, that is not prime
is called a composite number. 18. 307 is a prime number. Its factors are only 1 and
307.
Copyright © 2020 Pearson Education, Inc. 1
