Chapter 1
Section 4.
No. 4 7r3s(4rs
+ 1 -5rs2)
No. 6 (y
- 2)(4y - 5)
No. 8 2(z
+ 4)(z - 2)
No. 10 (a + 3)(5a2
+ 31a + 46)
No. 12 (5a - 3)(2B
+ 7)
No. 14 (3 - m2)(5
- r2)
No. 16 Both are correct
No. 18 8(h - 8)(h + 5)
No. 20 9y2(y -
5)(y - 1)
No. 22 (7m - 5r)(2m + 3r)
No. 24 (4s + t)(3s - t)
No. 26 (5a + m)(6a - m)
No. 28 3x3(3x
- 5z)(2x + 5z)
No. 30 (4p - 5)2
No. 32 5(2p - 5q)2
No. 34 (3mn - 2)2
No. 36 (2p + q - 5)2
No. 38 (4q + 5)(4q - 5)
No. 40 9(2z + 3y2)(2z
- 3y2)
No. 42 (p - 2q + 10)(p -
2q - 10)
No. 44. (m2 +
9)(m + 3)(m - 3)
No. 46. (c)
No. 48 (r + 3)(r2 -
3r + 9)
No. 50 (2m - 3n)(4m2
+ 6mn + 9n2)
No. 52 27(z + 3y)(z2
- 3zy + 9y2)
No. 54. b(b2 +
9b + 27)
No. 56 (5 - 4a + b)(25 +
20a - 5b + 16a2 - 8ab + b2)
No. 64 (a2 - 8)(a2
+ 6)
No. 66 z(8z - 3)(6z - 5)
No. 68 (18 - 5p)(17 - 4p)
Section 5
No. 2 x not equal
to -3
No. 4 x not equal
to 1/2
No. 6 no restrictions
No. 12 2/3
No. 14 -8/(y + 2)
No. 16 4y + 8
N0. 18 (r + 2)/(r + 4)
No. 20 (2m + 3)/(4m + 3)
No. 22 1/(4r3)
No. 24 1
No. 26 (m - 5)/16
No. 28 2/(r + 2)
No. 30 (x - 4)/(x - 5)
No. 32 (y + 3)/(y + 4)
No. 36 x - y
No. 40 47/20p
No. 42 12/5
No. 44 (27 - 2r)/3r
No. 46 101/12p
No. 48 (a - b)/a2
No. 50 (2m2 +
2)/[(m - 1)(m + 1)]
No. 52 2q/(p - q) or -2q/(q
- p)
No. 54 (-2m - 6)/(3m - 4)
or (2m + 6)/(4 - 3m)
No. 56 (17p - 4)/[(2p + 1)(p
- 5)(3p - 2)]
Section 7
No. 2 (b)
No. 4 (d)
No. 6 (a)
No. 8 (e)
No. 10 Fourth root of p5
No. 12 Seventh root of (5r
+ 3t)4
No. 14 -z5/4
No. 16 21/2my5/2
No. 18 (d)
No. 20 21/221/3
= 25/6 = sixth root of 25
No. 22 3
No. 24 7
No. 26 3 times square root
of 5
No. 28 5 times cube root
of 2
No. 30 -3 times fourth root
of 3
No. 32 negative of cube root
of 12 divided by 2
No. 34 fourth root of 24
divided by 2
No. 36 15 times cube root
of 75
No. 38 (2m3n2)times
square root of (6n)
No. 40 (-2a2b)
times cube root of b
No. 42 (x2yz2)
times fourth root of (y3z)
No. 44 cannot simplify further
No. 46 Square root of 15p
divided by 3p
No. 48 (gh2) times
square root of (ghr) divided by r2
No. 62 7 times cube root
of 3
No. 64 2 times square root
of 3
No. 66 13 times cube root
of 4 divided by 6
No. 68 -7
No. 70 10
No. 72 11 + 4 times square
root of 6
No. 74 5 times square root
of 6
No. 78 (- square root of
21 - 7)/4
No. 80 (-7 + square root
of 7 + 2 times square root of 14 - 2 times square root of 2)/2
No. 82 [square root of r(3
+ square root of r)]/(9 - r)
No. 84 {3m[2 - square root
of (m + n)]}/(4 - m - n)
No. 90 |a + 2b|
No. 92 r + 2s
No. 94 -2/[3(1 + square root
of 3)]
No. 96 p/(square root of
p - p)
No. 98 (-p2 +p
+1)/{p + p2 -2 times square root of [p(p2 -1) -1]}
Section 8
No. 4 real
No. 6 imaginary
No. 8 imaginary
or complex
No. 10 13i
No. 12 -15i
No. 14 -i times square root
of 95
No. 16 -7 + 10i
No. 18 -11 - 2i times square
root of 6
No. 20 -20
No. 22 quare root of 10
No. 24 6 + 4i
No. 26 1 + 2i
No. 28 -10 + i
No. 30 17 + i
No. 32 3 + 4i
No. 34 52
No. 36 18
No. 38 53i
No. 40 1
No. 42 -i
No. 44 i
No. 46 -i
No. 48 -1
No. 50 -i
No. 54 (3 - 4i)/5
No. 56 (26 + 7i)/29
No. 58 -1 - 2i
No. 60 (-11 + 60i)/61
No. 62 7i/3
Chapter 2
Section 1
No. 8 identity
{all real numbers}
No. 10 conditional {-17/2}
No. 12 contradiction
No. 14 equivalent
No. 16 not equivalent
No. 20 {3}
No. 22 {5/12}
No. 24 {-6/11}
No. 26 {-10/19}
No. 28 {-5}
No. 30 {1/12}
No. 32 {-48/71}
No. 34 {-1}
No. 36 No Solution
No. 38 {-11/5}
No. 40 No Solution
No. 42 {-16/3}
No. 44 {20}
Section 2
No. 22 6 cm
No. 24 width: 3 mm;
length: 7 mm
No. 26 4 ft
No. 28 96
No. 30 400/3 liters
No. 32 9.1 years
No. 34 1 hour, 8 minutes,
41.3 seconds
No. 36 50 miles
No. 38 560 km per hour
Section 3
No. 6 {+ or -
5}
No. 8 {+ or -
4 times the square root of 3}
No. 10 {+ or - 10i}
No. 12 {-2 + or - square
root of 7}
No. 14 {(-1 + or - 2 time
square root of 5)/4}
No. 16 {-4, 2}
No. 18 {2.5 + or - i times
square root of 2}
No. 20 {-6, 1}
No. 22 {-4 + or - square
root of 3}
No. 26 Incorrect as b = 0
No. 28 {(3 + or - square
root of 17)/2}
No. 30 {(7 + or - square
rot of 5)/22}
No. 32 {1 + or - 2i}
No. 34 {(-3 + or - 3 time
square root of 129)/16}
No. 36 {-1/4, 3}
No. 38 {1, -1/2, + or - (square
root of 3)/2 times i}
No. 40 {-3, 3/2, + or - (3
times square root of 3)/2 times i}
No. 42 {4, -2 + or - 2i times
square root of 3}
Section 4
No. 6 50 meters
by 100 meters
No. 10 1 ft
No. 16 3 mph
No. 20 5 ft
Section 5
No. 10 {-5, 3}
No. 16 {-5/2, 1/9}
No. 20 {3}
No. 22 {-1, 3}
No. 24 {8}
No. 28 {2}
No. 30 {5/4}
Section 7
No. 2 J
No. 4 H
No. 6 D
No. 8 G
No. 10 C
No. 14 (- infinity, 1]
No. 16 (- infinity, infinity)
No. 18 (- infinity, 15/7)
No. 20 [1/2, infinity)
No. 22 [-3/2, 3]
No. 24 (-1, -1/6)
No. 26 (-13/4, 3/4)
No. 30 [15, infinity}
No. 34 (- infinity, -4) U
(4, infinity)
No. 36 (-4, -2)
No. 38 (-4, 3)
No. 40 [-10/3, -1]
No. 42 Null
No. 44 Null
No. 46 (- infinity, -2 -square
root of 3) U (-2 + square root of 3, infinity)
No. 48 (- infinity, -1) U
(4, infinity)
No. 50 (-2, 2)
Section 8
No. 10 {-7/4, 3/4}
No. 12 {4/3, 10/3}
No. 14 {-16, 12}
No. 16 {1/8, 7/8}
No. 18 {7/3, 3}
No. 20 {1/4}
No. 22 {1/5, 7}
No. 24 {0, 1}
No. 26 {2}
No. 36 (- infinity, -5] U
[5, infinity)
Chapter 3
Section 1
No. 6 Domain:
{Pi, square root of 2, 7}; range: {-3, 5, cube root of 12}
No. 8 Domain:
{- infinity, infinity}; range {- infinity, infinity}
No. 10 Domain: {- infinity,
infinity}; range {- infinity, infinity}
No. 12 Domain: {- infinity,
infinity}; range: {- infinity, 0]
No. 16 (a)
10 (b) (-1, -1)
No. 18 (a)
3 times square root of 41 (b) (0, 5/2)
No. 20 (a)
3 times square root of 55 (b) [2 times
square root of 7, (7 times square root of 3)/2]
No. 26 yes
No. 30 yes
No. 34 (-5, 3)
No. 40 x2 + y2
= 81; Domain: [-9, 9]; Range: [-9, 9]
No. 44 (x - 4)2
+ (y - 3)2 = 25; Domain: [-1, 9]; Range: [-2, 8]
No. 52 (-4, 3); r =
3
No. 54 (6, -5); r =
6
No. 56 (-2, 0); r =
5
Section 2
No. 2 yes
No. 8 yes
No. 10 yes
No. 12 yes
No. 18 18
No. 20 52
No. 22 h2 + 3
No. 24 390
No. 44 [-6, infinity);
[0, infinity)
No. 46 (- infinity, infinity);
(- infinity, infinity)
No. 48 [-4, 3]; [-5,
6]
No. 52 (- infinity,
infinity); (- infinity, infinity)
No. 54 (- infinity,
infinity); [0, infinity)
No. 56 (- infinity, 3];
[0, infinity)
No. 58 [-11, 11]; [-11,
0]
No. 60 (- infinity, o) U
(0, infinity)
No. 62 (- infinity,
infinity); (- infinity, infinity)
No. 64 (a) (- infinity,
1] (b) [4, infinity) (c)
[1, 4]
No. 66 (a) none
(b) (- infinity, infinity) (c) none
No. 68 (a) (3, infinity)
(b) (- infinity, 3) (c) (-3, 3]
Section 3
No. 8 (-
infinity, infinity); (- infinity, infinity)
No. 10 (- infinity,
infinity); (- infinity, infinity)
No. 12 (- infinity,
infinity); (- infinity, infinity)
No. 14 (- infinity,
infinity); {3}
No. 16 (- infinity,
infinity); (- infinity, infinity)
No. 18 C
No. 20 B
No. 28 1
No. 30 0
No. 32 0
No. 34 Undefined
No. 40 (-2, 8), (-1,
7)
No. 42 (3, -4), (6,
-5)
No. 44 (9,4, 2), (9/4,
3)
Section 4
No. 6 x + y =
6
No. 8 3x - 4y
= -24
No. 10 y = 1
No. 12 y = -x + 7
No. 14 y = 2x + 4
No. 16 y = 7
No. 18 (a) D
(b) B (c) A (d) C
No. 22 slope: -2; y-intercept:
7
No. 24 slope: -2/3;
y-intercept: 16/3
No. 26 slope: 1/2;
y-intercept: 0
No. 28 2x - y = 8
No. 30 3x + 8y = -6
No. 32 y = -4
No. 34 (a) 2
(b) -6
Section 5
No. 2 G
No. 4 I
No. 6 E
No. 8 C
No. 10 D
No. 12 (1, 1); (0,0)
No. 14 (- infinity,
infinity); (- infinity, infinity)
No. 16 [0, infinity);
(- infinity, infinity)
No. 18 (- infinity,
infinity); (- infinity, 0]
No. 20 (- infinity,
infinity); [-3, infinity)
No. 22 [-1, infinity);
(- infinity, infinity)
No. 24 (- infinity,
infinity); (- infinity, 0]
No. 26 (- infinity, 1];
[0, infinity)
No. 28 [0, infinity);
[4, infinity)
No. 30 [-3, infinity);
[0, infinity)
No. 32 [-3, infinity);
[0, infinity)
No. 36 (a) -7
(b) -3 (c) -2 (d)
2
No. 44 f(x) = -1 if x is
less than or equal to 0 and 1 if x > 0
Section 6
No. 8 (a)
(-6, -1) (b) (6, 1) (c)
(6, -1)
No. 10 (a) (-8, 0)
(b) (8, 0) (c) (8, 0)
No. 14 y-axis
No. 16 x-axis, y-axis, origin
No. 18 origin
No. 20 none of these
Section 7
No. 2 false
No. 4 true
No. 6 -7x + 7;
x + 5; 12x2 -27x + 6; (6 - 3x)/(-4x + 1);
all domains are (- infinity, infinity) except f/g which is
(- infinity, 1/4) U (1/4, infinity)
No. 8 5x2
-x -1; 3x2 +5x -5; 4x4 - 10x3
- x2 +13x - 6; (4x2 + 2x - 3)/(x2
+13x - 6); all domains are
(-infinity, infinity) except f/g which is (- infinity, 1) U (1, 2)
U (2, infinity)
No. 10 square root of (5x
- 4) + square root of (3x - 1); square root of (5x - 4) - square
root of (3x - 1);
Square root of [(5x - 4)(3x - 1)]; square root of [(5x - 4)/(3x -1)]
No. 12 161
No. 14 -714
No. 16 18/7
No. 18 20k2 +
8k + 4
No. 20 3432
No. 22 814
No. 24 1
No. 26 3/2 or 1.5
No. 28 2
No. 30 3
Chapter 4
Section 1
No. 16 vertex: (-4,
0); axis: x = -4; Domain:
(- infinity, infinity); Range: [0, infinity)
No. 18 vertex: (5,
-4); axis: x = 5; Domain:
(- infinity, infinity); Range: [-4, infinity)
No. 24 vertex: (-3,
-4); axis: x = -3; Domain:
(- infinity, infinity); Range: [-4, infinity)
Section 2
No. 6 x2
+ 5x + 7 + 4/(x - 3)
No. 8 3x2
+ 3x - 1 + 1/(x - 1)
No. 10 x3 -5x2
+ 5x - 8
No. 12 (1/3)x2
- (1/9)x + 1/(x - 1/3)
No. 14 f(x) = (x + 4)(2x2
- 5x + 4) - 6
No. 16 f(x) = (x - 2)(-4x2
-6x - 15) - 40
No. 18 f(x) = (x + 3)(2 x3
- 5x2 + 3) - 9
No. 20 0
No. 22 127
No. 24 -2
No. 26 793
No. 28 -1
Section 3
No. 12 1, -2.5 + or - (square root of 5)/2
Chapter 5
Section 2
No. 56 (a) 3727 million which is off by about 27 million (b) 5342 million (c) 6395 million+-