Chapter 2

41⁵

7⁹

18

9

16

23

86

1

81

75

64

216

64

81

33

10

40

9

The terms are 4x, 3b, and 2. The coefficients are 4, 3, and 2.

The terms are 9a, 13a², and a³, The coefficients are 9, 13, and 1.

9, 15; 2x³ and 8x³, y², and 11y²

4x³ and 6x³; 8x² and 3x²; 19 and 24

16x + 17

17y + 7

4x² + 14x

12y² + 15y

w − 5

l + 2

6q − 7

4n + 8

no

yes

yes

yes

x + 1 = 7; x = 6

x + 3 = 4; x = 1

x = 13

x = 5

y = 28

y = 46

x = 22

y = 4

a = 37

n = 41

7 + 6 = 13

8 + 6 = 14

6 ⋅ 9 = 54

21 ⋅ 3 = 63

2(x − 5) = 30

2(y − 4) = 16

x + 7 = 37; x = 30

y + 11 = 28; y = 17

z − 17 = 37; z = 54

x − 19 = 45; x = 64

Divisible by 2, 3, 5, and 10

Divisible by 2 and 3, not 5 or 10.

Divisible by 2, 3, not 5 or 10.

Divisible by 3 and 5.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96

1, 2, 4, 5, 8, 10, 16, 20, 40, 80

composite

prime

2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 5, or 2⁴ ⋅ 5

2 ⋅ 2 ⋅ 3 ⋅ 5, or 2² ⋅ 3 ⋅ 5

2 ⋅ 3 ⋅ 3 ⋅ 7, or 2 ⋅ 3² ⋅ 7

2 ⋅ 3 ⋅ 7 ⋅ 7, or 2 ⋅ 3 ⋅ 7²

2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 5, or 2⁴ ⋅ 5

2 ⋅ 2 ⋅ 3 ⋅ 5, or 2² ⋅ 3 ⋅ 5

2 ⋅ 3 ⋅ 3 ⋅ 7, or 2 ⋅ 3² ⋅ 7

2 ⋅ 3 ⋅ 7 ⋅ 7, or 2 ⋅ 3 ⋅ 7²

36

72

60

105

440

360

16 minus 9, the difference of sixteen and nine

5 times 6, the product of five and six

28 divided by 4, the quotient of twenty-eight and four

x plus 8, the sum of x and eight

2 times 7, the product of two and seven

fourteen is less than twenty-one

thirty-six is greater than or equal to nineteen

3 times n equals 24, the product of three and n equals twenty-four

y minus 1 is greater than 6, the difference of y and one is greater than six

2 is less than or equal to 18 divided by 6; 2 is less than or equal to the quotient of eighteen and six

a is not equal to 7 times 4, a is not equal to the product of seven and four

equation

expression

expression

equation

3⁷

x ⁵

125

256

5

34

58

6

13

4

35

10

41

81

149

50

22

26

144

32

27

21

41

9

225

73

54

15x², 6x, 2

10y³, y, 2

8

5

x³, 8x³ and 14, 5

16ab and 4ab; 16b² and 9b²

13x

26a

7c

12x + 8

10u + 3

12p + 10

22a + 1

17x² + 20x + 16

8 + 12

14 − 9

9 ⋅ 7

36 ÷ 9

x − 4

6y

8x + 3x

$\frac{y}{3}$

8 (y − 9)

5 (x + y)

b + 15

b − 4

2n − 7

He will pay $750. His insurance company will pay $1350.

x + 2 = 5; x = 3

x + 3 = 6; x = 3

a = 16

p = 5

r = 24

x = 7

p = 69

d = 67

y = 22

u = 30

f = 178

n = 32

p = 48

y = 467

8 + 9 = 17

23 − 19 = 4

3 ⋅ 9 = 27

54 ÷ 6 = 9

2(n − 10) = 52

3y + 10 = 100

p + 5 = 21; p = 16

r + 18 = 73; r = 55

d − 30 = 52; d = 82

u − 12 = 89; u = 101

c − 325 = 799; c = 1124

$1300

$460

2, 4, 6, 8, 10 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48

4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48

6, 12, 18, 24, 30, 36, 42, 48

8, 16, 24, 32, 40, 48

10, 20, 30, 40

Divisible by 2, 3, 4, 6

Divisible by 3, 5

Divisible by 2, 3, 4, 6

Divisible by 2, 3, 4, 5, 6, 10

Divisible by 2, 4

Divisible by 3, 5

Divisible by 2, 5, 10

Divisible by 2, 5, 10

Divisible by 3, 5

1, 2, 3, 4, 6, 9, 12, 18, 36

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

1, 2, 3, 4, 6, 8, 12, 18, 24, 36, 48, 72,144

1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 49, 84, 98, 147, 196, 294, 588

prime

composite

prime

composite

composite

composite

2 ⋅ 43

2 ⋅ 2 ⋅ 3 ⋅ 11

3 ⋅ 3 ⋅ 7 ⋅ 11

5 ⋅ 23

3 ⋅ 3 ⋅ 5 ⋅ 5 ⋅ 11

2 ⋅ 2 ⋅ 2 ⋅ 7

2 ⋅ 2 ⋅ 2 ⋅ 3 ⋅ 7

17 ⋅ 23

2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 3 ⋅ 3 ⋅ 3

2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 5

2 ⋅ 3 ⋅ 5 ⋅ 5

3 ⋅ 5 ⋅ 5 ⋅ 7

2 ⋅ 2 ⋅ 3 ⋅ 3

2 ⋅ 5 ⋅ 5 ⋅ 7

24

30

120

300

24

120

420

42

120

40

the product of 3 and 8

the quotient of 24 and 6

50 is greater than or equal to 47

The sum of n and 4 is equal to 13

equation

expression

2³

x ⁶

8 ⋅ 8 ⋅ 8 ⋅ 8

y ⋅ y ⋅ y ⋅ y ⋅ y

81

128

20

18

74

31

58

26

12n²,3n, 1

6

3, 4, and 3x, x

24a

14x

12n + 11

10y² + 2y + 3

x − 6

3n ⋅ 9

5(y + 1)

c + 3

x + 3 = 5; x = 2

6

11

23

34

7 + 33 = 44

4 ⋅ 8 = 32

2(n − 3) = 76

x + 8 = 35; x = 27

q − 18 = 57; q = 75

h = 42

z = 33

q = 8

v = 56

3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48

8, 16, 24, 32, 40, 48

2, 3, 6

2, 3, 5, 6, 10

1, 2, 3, 5, 6, 10, 15, 30

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180

prime

composite

2 ⋅ 2 ⋅ 3 ⋅ 7

2 ⋅ 5 ⋅ 5 ⋅ 7

45

175

Answers will vary

fifteen minus x

equation

36

5

45

125

36

x + 5

3(a − b)

n = 31

y − 15 = 32; y = 47

4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48

2³ ⋅ 3³ ⋅ 5