SOLUTIONS TO PROBLEMS

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;  (4x + 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+-