ch. 0 review of algebra - جامعة...

Ch. 0 Review of Algebra

0.1 Sets of Real Numbers

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Provide an appropriate response.

1) True or False: 6 is a rational number.

2) True or False: 0 is an integer.

3) True or False: 3 is an irrational number.

4) True or False: 46 is an integer.

5) Given the numbers 4, -7, 34, π, 0, - 0.2, list those that are integers.

6) Given the numbers 4, -7, 34, π, 0, - 0.2, list those that are rational.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

7) How many of the following statements are correct?I. -4 is a rational number

II. 21 is an integer

III. 0 is an integer

IV. -16 is a rational number

A) exactly one of them

B) exactly two of them

C) exactly three of them

D) all of them

E) none of them

8) Given the numbers 4, -7, 34, π, 0, - 0.2, how many are irrational?

A) exactly one

B) exactly two

C) exactly three

D) exactly four

E) none of the above


9) .7 is a rational number. Please explain why this is true or false.

10) True or False: e is a rational number.

11) How many rational numbers are there between 0 and 1?

0.2 Some Properties of Real Numbers



1) State the property of real numbers that is being used: 4(x + y) = 4x + 4y

2) State the property of real numbers that is being used: 2(ab) = (2a)b

3) State the property of real numbers that is being used: 7 + ab = ab + 7

4) State the property of real numbers that is being used: (4 + x) + y = 4 + (x + y)


5) What property of real numbers allows us to write a(b + c) = a(c + b)?

A) commutative

B) distributive

C) identity

D) associative


6) The additive inverse of 2 is

A) 12.

B) - 12.

C) -2.

D) -1.



7) Find the additive inverse of 3.

8) Find the multiplicative inverse of 3.

9) State the property of real numbers that is used in the equality (e + a)b = e × b + a × b.


10) What property of real numbers allows us to write (e + a)b = eb + ab?

A) closure

B) commutative

C) associative

D) distributive



11) Simplify: -3 + 8

12) Simplify: -6 - 2

13) Simplify: -4 - (-10)

14) Simplify: (-3)(6)

15) Simplify: (-4)(-2)

16) Simplify: (-15) ÷ (-5)

17) Simplify: 4 ÷ (-2)

18) Simplify: 7(x - 2)

19) Simplify: -(4 - x)

20) Simplify: 0(2 + x)

21) Simplify: 34 · 5x

22) Simplify: (7x) 47x

23) Simplify: -20y-5x

24) Simplify: 38 + 5

8


6

26) Simplify: 310 - 4

15


7

28)

Simplify:

2349

29)

Simplify: x4y

30)

Simplify:

2xy

31) Simplify: 04


32) -9 - (-3) =

A) 6 B) -6 C) 10 D) 12 E) -12

33) -2 + (-7) =

A) -5 B) 5 C) 14 D) 9 E) -9

34) 4 -3(4) + 2(5) =

A) -8 B) -38 C) -68 D) -88 E) -200

35) -3(x - y) =

A) -3x + 3y B) 3x - 3y C) -3x - 3y D) 3x - y E) -3x + y

36) 45 + 3

10 =

A) 1 B) 710

C) 1110

D) 715

E) 750

37) 210 - 3

25 =

A) 225

B) - 325

C) 725

D) - 115

E) - 3125


38) Simplify: (-4) ÷ (-2 - 10)

39) Simplify: 2x - 46 - 3x

40)

Simplify: 2 + 1

3

3 - 23

41) Simplify: -2(3 - 5x)

42)

Simplify:

(x + 1)214

43) Simplify: 35 ÷ 8

9

44) True or False: 311

77 = 3

11

45) Simplify: 7 ÷ 35

46) Simplify: 23 - 5

2

0.3 Exponents and Radicals



1) Find the value and simplify: 36


3) Find the value and simplify: 3-64

4) Find the value and simplify: 3 827

5) Find the value and simplify: 93/2

6) Find the value and simplify: 4-1/2

7) Find the value and simplify: (34)3/4

8) Find the value and simplify: 254 -1/2

9) Find the value and simplify: (-8)4/3


2/3

11) Find the value and simplify: (16)-3/2

12) Find the value and simplify: (32)3/5

13) Simplify: 20

14) Simplify: 5y10

15) Simplify: 3128

16) Simplify: (16x4)1/2

17) Simplify: 64x3

27

2/3

18) Simplify: x6x2(3x3)

19) Simplify: (x4)3

20) Simplify: (3x)3

21) Simplify and express your answer in terms of positive exponents: t6

t3

22) Simplify and express your answer in terms of positive exponents: z5

z6

23)

Simplify and express your answer in terms of positive exponents: x2y

5

24) Simplify: x4y3 5

25) Simplify: y5(y3)2

26) Simplify and express your answer in terms of positive exponents: x12

x4x4

27)

Simplify and express your answer in terms of positive exponents: a2b3c3

4

28) Simplify and express your answer in terms of positive exponents: (x5)7

y5y7

29) Simplify and express your answer in terms of positive exponents: (2x-3y2)5

30) Simplify and express your answer in terms of positive exponents: (4x)-2

31) Simplify and express your answer in terms of positive exponents: x-5

(x4) -2

32) Simplify and express your answer in terms of positive exponents: x-3y-2

x2y-7

33)

Simplify and express your answer in terms of positive exponents: x-1

y-1

-2

34)

Simplify and express your answer in terms of positive exponents: 3x-4yz2

-3

35) Simplify and express your answer in terms of positive exponents: (2x2y-3)2

x2

36) Simplify and express your answer in terms of positive exponents; rationalize the denominator to avoid

fractional exponents in the denominator: 3xx

37) Simplify and express your answer in terms of positive exponents; rationalize the denominator to avoid

fractional exponents in the denominator: x(x1/3y1/5)6

38) Rationalize the denominator and simplify: 37

39)

Rationalize the denominator and simplify: 83x

40)

Rationalize the denominator and simplify: 235

732

41) Rationalize the denominator and simplify: 35 6

42) Rationalize the denominator and simplify: 502

43)

Rationalize the denominator and simplify: 2

53x2


44) (x6)3(x2) =

A) x11 B) x36 C) x20 D) x81 E) x54

45) 2x3

y2

4=

A) 2x7

y6B) 2x

12

y8C) 16x12

y8D) 16x

12

y2E) 16x

7

y6

46) x-4x-2

y-7y5 =

A) 1x6y2

B) x6

y2C) y

2

x6D) x6y2 E) x8y35

47) 3ab-2

a-1b3 =

A) 3a5

b2B) 3a

2

b5C) 3a

bD) -3a2

b5E) 3b

48) x-3

y2z-2

-3=

A) yz5

x6B) x

6

yz5C) x

9z2

y2D) z6

x9y6E) x

9y6

z6

49) How many of the following are true?

I. y12y14

y12 = y14

II. 246 = 2

III. 63 = 3 7IV. (-1)3 - (-2)3 - ( 7)2 = 0

A) exactly one

B) exactly two

C) exactly three

D) exactly four

E) none of them

50) 8x6

-2/3=

A) 64x2

B) 4x4

C) x44

D) 4x4 E) 14x4

51) 132

-2/5=

A) - 1160

B) 14

C) 4 D) 12

E) 2

52) (16x-2)5/4=

A) 32x5/2

B) 20x3/4

C) 32x2

D) 132x5/2

E) x5/232

53) 2x3/4y1/2 4 =

A) 16x3y2 B) x3y216

C) 16x3y8 D) 16x19/4y9/2 E) 16x3/4y1/2

54)5(64)5/6 =

A) (64)5 B)63 C) 32 D)

52 E) 2


55) Evaluate: 37

33

56) Simplify: 316328

31735

57) Simplify: 3a3b2 3 2ab3c2 4

58) Simplify: 289 - x7y8 0

59) Simplify and express your answer in terms of positive exponents: x-5y3/5 10/3

60) Simplify and express your answer in terms of positive exponents:532x-10y15

61) Simplify and express your answer in terms of positive exponents: a5/3b3/4 5

a7/3 4

62) Write the following in radical form: a5/7

63)

Simplify and express your answer in terms of positive exponents: 32pq

34pq2

64)

Simplify the following; express your answer with no radical in the denominator: 316

32

65) Simplify the following; express your answer with no radical in the denominator:37a2b5

32a1b8

66) Simplify the following; express your answer with no radical in the denominator:

12p5q6

3pq2


6x2y4 2x3y2

3 xy2

68) Simplify the following; express your answer with no radical in the denominator:x-1/2

2


a2b

ab2

70)

Simplify; express the answer without radicals: 3a5b7

71)

Simplify; express the answer without radicals: 36ab5 3a2b

72) Simplify; x1/2 × x3/4

73) Simplify; express the answer without radicals: x3/2 y1/3

74)

Simplify; express the answer without radicals: 53s2t3

52s3t2

0.4 Operations with Algebraic Expressions



1) Simplify: (3x + 2y - 5) + (x - 4y + 2)

2) Simplify: 6x2 - 10x + 7 - (2x - x2 + 7)

3) Simplify: 2(-a - 2) + 3

4) Simplify: 7(x - y) - 4(y - x)

5) Simplify: (-a + b - c) - a + b

6) Simplify: 3 8x - (2x + 5)

7) Simplify: 3(x - 7) - 4(x2 - x) + 2(1 - x)

8) Simplify: 2 x - y2 - 3(2x - y2)

9) Simplify: - (6 + 2x) - 4(x - 2)

10) Simplify: 2 5 x - 2(x - 1) + 6 + 1

11) Multiply and simplify: (x + 1)(x + 4)

12) Multiply and simplify: (x - 5)(x + 2)

13) Multiply and simplify: (2y - 1)(3y + 4)

14) Multiply and simplify: (x - 3)(7 + x)

15) Multiply and simplify: (x + 5)2

16) Multiply and simplify: (t + 3)(t - 3)

17) Multiply and simplify: (2x - 1)2

18) Multiply and simplify: (x + 2)(x + 4)

19) Multiply and simplify: (y - 3)(y + 7)

20) Multiply and simplify: (z - 5)(z - 1)

21) Multiply and simplify: (3x + 4y)2

22) Multiply and simplify: (2t - 5)(2t + 5)

23) Multiply and simplify: (3x + 1)(2x - 4)

24) Multiply and simplify: (x3 - 9)(x3 + 9)

25) Multiply and simplify: (x + 4)3

26) Multiply and simplify: (2x - 1)3

27) Multiply and simplify: 4x(x + 1)2

28) Multiply and simplify: (4x - 3)(x2 - x + 2)

29) Multiply and simplify: (x + 2)(x - 2)(x2 + 4)

30) Perform the operations and simplify: x(x + 4) - (x + 2)(x - 1)

31) Perform the operations and simplify: x(x + 4) - (x + 4)(x - 5)

32) Divide and simplify: (10x + 20y) ÷ 5

33) Divide and simplify: (x2 - 6x + 2) ÷ x

34) Divide and simplify: (8x3y2 - 2x2y - x) ÷ (2xy)

35) Divide and simplify: (x4 + (2xy2)2 - 3y) ÷ (xy)2

36) Divide and simplify: (x2 - 3x - 4) ÷ (x - 2)

37) Divide and simplify: (4x3 + 5x - 3) ÷ (2x + 1)


38) Simplify: -2 10x - 3(x - 2y)

A) 12y - 2x B) 2x + 2y C) -2x + 6y D) -14x - 12y E) -2x - 2y

39) Simplify: 2 3x - 2 4(x - 2) + 1 + x

A) -10x + 28 B) -9x + 4 C) 8x + 28 D) -11x + 20 E) -9x + 28

40) Simplify: (x + y + z) - (x + 3y - 7z) - (-3x - y + 8z)

A) -x + 3y + 2z B) -x + 2z C) 3x - y D) y - 3z E) y - 3x

41) (4x - 3)(2x + 1) =

A) 8x2 + 7x + 3 B) 8x2 - 7x - 3 C) 8x2 - 2x - 3 D) 8x2 + 2x - 3 E) 6x - 2

42) (x + 1)(x2 + 3x - 5) - 3x2 =

A) x3 + 4x2 - 2x - 5

B) x3 + x2 - 2x - 5

C) -2x3 + 4x2 - 2x - 5

D) -2x2 + 4x - 4

E) -3x5 - 12x4 + 6x3 + 15x2

43) (2x2 - 1)(x3 - 3x + 6) =

A) 2x5 - 7x3 + 12x2 - 3x + 6

B) 2x5 - 7x3 + 12x2 - 3x - 6

C) 2x5 - 7x3 + 12x2 + 3x - 6

D) 2x6 - x3 + 6x2 + 3x - 6

E) 2x6 - 7x3 + 12x2 + 3x - 6

44) (x - 4)2 =

A) x2 - 16 B) x2 - 4x + 16 C) x2 + 4x - 16 D) x2 - 8x + 16 E) x2 + 8x + 16

45) (x - 2)(x + 2) =

A) x2 + 4 B) x2 - 4 C) x2 - 2 D) x2 + 2 E) x2 - 2

46) (x + 6)(x - 2) =

A) x2 + 4x - 12 B) x2 - 4x - 12 C) x2 + 8x - 12 D) x2 - 8x - 12 E) x2 + 8x + 12

47) (3t - 4)(4t - 5) =

A) 7t2 - 20

B) 12t2 + 20

C) 12t2 - t + 20

D) 12t2 + t + 20

E) 12t2 - 31t + 20

48) (x + 3)2 - (3 - x)2 =

A) 0 B) 2x2 C) 12x D) 2(x + 3)2 E) 18

49) (4 - 3x2y)(4 + 3x2y) =

A) 4 - 9x2y B) 16 - 9x4y C) 16 + 9x4y2 D) 16 - 9x4y2 E) 16 - 9x4y4

50) (x + 1)(x - 1)( x2 - 1) =

A) x4 - 1

B) x4 + 1

C) x4 - 2x2 + 1

D) x4 + 2x2 + 1


51) (2x + 3)3 =

A) 2x3 + 18x2 + 54x + 27

B) 8x3 + 36x2 + 54x + 27

C) 8x3 + 18x2 + 54x + 27

D) 8x3 + 12x2 + 18x + 27

E) 8x3 + 3x2 + 3x + 27

52) x3 + 4x2 - 12x

4x

A) x24 + x - 3

B) x3 - 11x

C) x3 + 4x2 - 3

D) 5x2 - 12x

E) x24 - 4x2 - 12x

53) 10x6 - 6x4 + 4x3

2x2

A) 68x5y

B) 9y - 3y4 C) 98x5

- y3

4x4D) 9y

8x3 - y

2

4x4E) 9y

8x2 - y

2

4x3

54) (x2 + 4x + 7) ÷ (x - 3) =

A) x - 4 + 26x - 3

B) x + 7 + 28x - 3

C) x - 5 - 16x - 3

D) x + 3 - 5x - 3

E) x + 1 + 4x - 3

55) (x3 + 3x - 6) ÷ (x + 2) =

A) x2 + 3x - 3

B) x2 + 1 - 8x + 2

C) x2 + x - 2 - 2x + 2

D) x2 + x + 7 + 8x + 2

E) x2 - 2x + 7 - 20x + 2


56) Add the algebraic expressions:35x2y + 7

3xy2 - 11x + 12y + 8

3xy2 + 7

5x2y + 8x - 11xy

57) Add the algebraic expressions:57a3bc - 3

7ab2 + 8

5a2b + 11

5a - b + 3

7ab2 - 5

7a3bc + 2

5a2b - 11

5b - 1

5a

58) Subtract the algebraic expressions:35x2y + 7

3xy2 - 11x + 12y - 8

3xy2 + 7

5x2y + 8x - 11xy

59) Subtract the algebraic expressions:57a3bc - 3

7ab2 + 8

5a2b + 11

5a - b - 3

7ab2 - 5

7a3bc + 2

5a2b - 11

5b - 1

5a

60) Simplify: 7 2a2(a + b) - 8b(a - b)

61) Simplify: 23

32a(a - b) - 3b(a + b)

62) Simplify: 5 a(a + b) - 3b(b - a) - 3ab(1 - a)

63) Multiply and simplify: (t + 2s)(t - 2s)

64) Multiply and simplify: (a + b - c)(a - b + c)

65) Multiply and simplify: 13x + 2

3y 1

7x - 2

7y

66) Multiply and simplify: (a + b)(a - b)(2a + b)

67) Multiply and simplify: (x + 1)2(x - 1)2

68) Simplify: ( a2 + b2 - a)( a2 + b2 + a)

69) Divide the polynomial x3 + x2 + 2x + 1 by x - 1 to give the quotient and remainder.

70) Divide the polynomial 2x2 + 3x + 5 by x - 2 to give the quotient and remainder.

71) Divide the polynomial x2 + 3x + 5 by 2x + 1 to give the quotient and remainder.

72) Divide the polynomial 2x3 + 3x2 + 5x + 7 by 2x2 + 5x + 1 to give the quotient and remainder.

73) Divide the polynomial x3 + 3x2 + 5x + 7 by 2x2 - 1 to give the quotient and remainder.

74) Simplify: (a - b)2(a + 2b)

75) Simplify: (2a - 3b)3

76) Simplify: a a2 - b2 + b a(b - a2) + a3b

0.5 Factoring



1) Completely factor: 5x - 5

2) Completely factor: 3ax + 9ay

3) Completely factor: 4xy3 + 6xy2 - 2xy4

4) Completely factor: x7/5y3 - 35x2/5y4

5) Completely factor: x2 - 36

6) Completely factor: x2 + 4x + 3

7) Completely factor: 4y2 - 25

8) Completely factor: x2 - 10x + 16

9) Completely factor: t2 - 8t - 9

10) Completely factor: x2 + 6x + 9

11) Completely factor: (6x + 15)2

12) Completely factor: x2 + x - 12

13) Completely factor: 2y2 + 7y + 3

14) Completely factor: 6z2 - 13z - 5

15) Completely factor: 4x2 + 5x - 6

16) Completely factor: 16t2 + 8t + 1

17) (x3 - 9x) + (36 - 4x2)

18) (y4 + 2y3 + y2) - (4y2 + 8y +4)

19) Completely factor: 2x2 - 8

20) Completely factor: x3 + 5x2 + 6x

21) Completely factor: 3x4 + 6x3 + 3x2

22) Completely factor: (x + 2)(x + 3) + (x + 2)(x + 4)

23) Completely factor: (x + 3)2 (x - 5)3 - (x + 3)(x - 5)4


25) Completely factor: x6 - 27y3

26) Completely factor: x4 - 1

27) Completely factor: x4 + 5x2 - 36


28) One factor of 2x2y3 - 4xy4 is

A) 4x2y4 B) 2x2y3 C) 2xy4 D) x - 2y E) 2y2 - 4

29) One factor of x2 + 8x - 20 is

A) x - 1 B) x - 2 C) x + 4 D) x + 5 E) x + 20

30) One factor of x2 - 12x + 36 is

A) x + 6 B) x - 6 C) x +1 D) x - 9 E) x - 4

31) One factor of 8x2 + 6x - 27 is

A) 4x - 9 B) 8x + 1 C) 2x - 27 D) 4x - 3 E) 2x - 3

32) One factor of 6x2 - 17x + 10 is

A) 2x - 5 B) 3x - 5 C) 6x + 5 D) x - 2 E) x + 2

33) One factor of x3 - 64 is

A) x2 + 4x + 16 B) x2 - 4x + 16 C) x2 + 16 D) x2 - 16 E) x + 4

34) One factor of x(y + 6) + 2(y + 6) is

A) x + 6 B) y + 2 C) x + 2 D) x + y E) y + 12

35) Factoring x4 - 81 gives

A) (x2 -9)(x2 - 9)

B) (x2 + 9)(x2 + 9)

C) (x2 + 9)(x + 3)(x - 3)

D) (x2 - 9)(x + 3)(x - 3)

E) (x + 3)2(x - 3)2

36) Factoring (x + 1)(x - 3) + (x + 7)(x - 3) gives

A) 2(x - 3)(x + 8)

B) 2(x - 3)(x + 4)

C) (x + 1)(x +7)(x - 3)

D) (x + 1)(x +7)(x - 3)2

E) (x -3)(2x - 2)

37) Factoring (x + 8)4(x + 2)3 - (x + 8)3(x + 2)4 gives

A) 6(x + 8)3(x + 2)3

B) 10(x + 8)3(x + 2)3

C) 2(x + 8)3(x + 2)3(x + 5)

D) 0



38) Completely factor: a3 - 8b3

39) Completely factor: p4 - 16

40) Completely factor: x4 - 8x

41) Completely factor: (2x + 1)(3x - 5) - (7x + 1)(3x - 5)

42) Completely factor: 2t2 + 8t + 6


44) Completely factor: -x2 - 2x + 3

45) Completely factor: 2x2 + 5x + 3

46) Completely factor: a4 - 8a2b2 - 9b4

47) Completely factor: x2y + 11xy2

48) Completely factor: a3 + (b - c)3

49) Completely factor: x-2 + 8x-1 - 20

0.6 Fractions



1) Perform the operation and simplify your answer: x + 7x · 63x + 21

2) Perform the operation and simplify your answer: z2 - 4z2 + 2z

· z2

z - 2

3) Perform the operation and simplify your answer: 3 - xx2 - x - 2

· x + 12x - 6

4) Perform the operation and simplify your answer: x2 - 3x + 2x2 - 7x + 12

· x2 - x - 6x2 + x - 2

5)

Perform the operation and simplify your answer:

x6y

6)

Perform the operation and simplify your answer: 6xy

7)


29x3y4

8)


2x - 2y3zx - y6z3

9)


xx2 - 42

(x + 2)2

10) Perform the operation and simplify your answer: 2x - 2x2 - 2x - 8

÷ x2 - 1x2 - 5x + 4

11)

Perform the operation and simplify your answer: x2 - 12x + 27

x2 - 81x2 + 9x

12) Perform the operation and simplify your answer: 2x - x

2

13) Perform the operation and simplify your answer: x2

x - 2 + x - 6x - 2

14) Perform the operation and simplify your answer: 42x - 1

+ xx + 3

15) Perform the operation and simplify your answer: 7x - 8y + 3

16) Perform the operation and simplify your answer: 3 + x - 2x + 3

17) Perform the operation and simplify your answer: xx2 - 9

- 2x3x - 9

18) Perform the operation and simplify your answer: x + 4x2 + 2x + 1

+ x - 2x2 + 5x + 4

19) Perform the operation and simplify your answer: 3 x(x - 1)

- x - 1x2(x + 1)

20) Perform the operation and simplify your answer: 5 - x5 - 1

21) Perform the operation and simplify your answer: xx - 4

+ 2x - 14 - x

22) Perform the operation and simplify your answer: 2x - 1

+ 3x2- 1

- 2x + 1

23)

Perform the operation and simplify your answer: 3 - 2

x4

24)

Perform the operation and simplify your answer: 1 + 1

x

2 - 1y

25)


ab + ba

ab - ba

26)

Perform the operation and simplify your answer: x

5x + x2

27)


1x + 2

3

9-4x26

28) Perform the operation and simplify your answer:

2x + 2

- 4x2 - 4

x - 8x - 2

29) Simplify into a single fraction and give your answer with positive exponents only: (x-1 + 4)-1x

30) Simplify into a single fraction and give your answer with positive exponents only: 1 + x-1

1 - x-2

31) Rationalize the denominator: 13 - 2

32) Rationalize the denominator: 35 + 3


33) How many of the following are true?

I. a + bxa + cy

= bxcy

II.1

12 + 1

3

= 2 + 3

III. abxacy = bxcy

IV. 1x - x - yx2

= x - x - yx2

A) None of them

B) Exactly one of them

C) Exactly two of them

D) Exactly three of them

E) all of them

34) Which of the following are true?

I.

1xy =

1xy

II. x + yy + x

+ x - yy - x

= 0

III. 1x · 1y = 1xy

A) none B) I only C) I and II only D) I and III only E) all of them

35) Simplify: x + y3 · 6x + 9y

x + y

A) 2x + 3 B) 2x + 3y C) -6x + 9y D) -(2x + 3y) E) 12x + 3y

36) 2x2 +5x - 3x2 - 8x + 16

÷ 4x2 - 1x2 - x - 12

=

A) (x + 3)2(x - 4)(2x + 1)

B) 2x2 - 3x +74x2 - 6x + 1

C) (2x - 1)2 (2x + 1)(x - 4)3

D) (x + 3)(x -3)2(x - 2)2

E) 2x4 + 3x3 - 35x2 - 57x +364x4 - 32x3 + 60x2 + 8x - 16

37) x2 - x - 6x2 + 8x + 16

÷ x2 - 9x2 - x - 20

=

A) (x + 2)(x + 3)(x - 3)2

(x - 5)(x + 4)3

B) (x + 2)(x - 3)(x - 5)(x + 4)

C) (x - 2)(x + 5)(x + 4)(x - 3)

D) (x + 2)(x - 5)(x + 4)(x + 3)

E) (x - 2)(x - 5)(x + 4)(x - 3)

38)

Simplify:

2x + 5y

2x - 5y

A) - 73

B) 2y + 5xxy(2y - 5x)

C) 2y + 5x2y - 5x

D) 2y - 5x2y + 5x


39)

Simplify:

5x3 - 3x2

x2 + 4x

A) 5 - 3x2x3

B) 2(5 - 3x)x2(x2 + 8)

C) (5 - 3x)(x2 + 8)2x4

D) 2(x + 2)x5(x + 4)

E) 1x5

40) 3x + 412

- 2x - 39

=

A) 24x + 136

B) 36x + 2436x

C) 24 - x36

D) x - 2436

E) x + 2436

41) xx - 3

- 4x - 2x3 - 3x2

=

A) -3x - 2x2(x - 3)

B) x2 - 4x - 2x2(x - 3)

C) x2 - 4x + 2x2(x - 3)

D) x3 - 4x - 2x2(x - 3)

E) x3 - 4x + 2x2(x - 3)

42) xx2 - 2x - 8

- 2x2 + 4x + 4

+ 3x - 4

=

A) 4(x2 + x + 3)(x + 2)2(x - 4)

B) 4(x2 + 3x + 5)

(x + 2)2(x - 4)

C) x2 + 6x + 14

(x + 2)(x - 4)

D) 4(x + 3)(x + 2)(x - 4)

E) 10(x + 2)(x - 4)

43) x-1 + x(1 - x-1) -1

=

A) 2x1 - x

B) x2 + 1

x(1 - x)

C) (x2 + 1)(x - 1)x2

D) 1 - x + x2 - x3x

E) 0

44) Rationalizing the denominator in 31 + 2

gives

A) 1 - 2 B) 4 - 3 2 C) -2 + 5 2 D) -3 +3 2 E) 6 - 4 2


45)

Simplify: a3 - 8b3

a2 - 5ab + 6b2

46) Simplify: x4 - 8xx3 + 2x2 + 4x

47) Simplify: 2x2 - 2

x3 - x2

48) Multiply and simplify: a2 - b2a + b

× a2 + 5ab + 3b2

a - b

49) Divide and simplify: a2 - b2a + b

÷ a2 + ab - 2b2

a2 + 2ab + b2

50) Divide and simplify: a + ba - b

÷ 2a + b(3a - b)

51) Divide and simplify:

x32y

3x6

5y2 × 2yx6

52) Divide and simplify: x + 1

y

x - 1y

53) Divide and simplify:

x2x - y

- x

y2x - y

+ y

54) Simplify: 1 + 1

1 + 1

1 + 1x

55) Perform the indicated operations and simplify: 2x - 12x - 4

+ 34x - 8

+ 5x - 13x - 6

56) Rationalize the numerator of 2x + 2h - 2xh

and simplify:

57) Simplify: 2x2 + 3

x2 + 1 + x2 + 1

58) Simplify: 1x + 1

+ 1x - 1

+ 1x2 + 1

59) Rationalize the denominator and simplify: 2 + x2 - x

60) Simplify: x2x + 2

+ 5x + 3x

2x2 + 2x

0.7 Equations, in Particular Linear Equations



1) Solve: 23x - 4 = 3

2) Solve: 6y7 = - 3

5

3) Solve: 3 - 2x = 4

4) Solve 2q - 1 = 2(1 - q)

5) Solve: 0.4x - 3 = 6

6) Solve: x = 2x - (6 - x)

7) Solve: 3z - 47

= 13

8) Solve: x2 + 3

4 = x

9) Solve: x3 - 1 = x

5

10) Solve: 2(t - 1) - 3(t - 4) = 4t

11) Solve: 3 2x - (1 + x) + 3(x - 2) = 0

12) Solve: 32(4x - 3) = 2 x - (4x - 3)

13) Solve: x - 43 - x + 2

3 = x - 27

4

14) Solve: x(x - 2) - (x + 1)2 = 3

15) Solve: (x + 1)2 - 2x = x2 + 2

16) Solve for x: a(2 -x) = 3b

17) Solve for x: ax + 3 = b(x +2)

18) Solve the formula h = katTL for L.

19) Solve the equation S = P(1 + rt) for t.

20) Solve the equation y = mx + b for x if m = -2, b = 3, and y = 4.

21) True or False: The equations x - 7 = 0 and x(x - 7) = 0 are equivalent.

22) True or False: The equations x - 7 = 0 and 3(x - 7) = 0 are equivalent.

23) The relationship between the temperature F on the Fahrenheit scale and the corresponding temperature C on

the Celsius scale is given by C100

= F - 32180

. Convert 77°F into a Celsius temperature.


24) Exactly how many of the following equations are guaranteed to be equivalent to x2 - 2x = 3?I. x(x - 2) = 3II. x - 2 = 3III. x3 - 2x2 = 3xIV. x2 - 2x + 3 = 0

A) one B) two C) three D) all E) none

25) Solve: 4x9 + 5x

-6 = - 3x

2 + 4

3

A) 56

B) 53

C) 65

D) 1918

E) 0

26) If mt + gt = 2(3 + t), solve for t.

A) 6 - m - g B) 6mg - 2

C) 6mg + 2

D) 6m + g - 2

E) 6m + g + 2

27) If x5 + x - 5

10 = 7, solve for x.

A) 4 B) 23

C) 3215

D) 6 E) 25

28) If A = p + prt, then r =

A) A - pp + t

B) Ap + pt

C) A + ppt

D) A - ppt

E) A - p - pt


29) Solve the equation: 0.4(x + 1.3) = 1.9

30) Solve the equation: 1.4( 0.2x + 1.3) = 0.5(0.1x + 4.56)

31) Solve the equation: 3x + 57

= 2(5 - x)4

32) Solve the equation: 5 7x - (2 - 3x) - 3 1 - (2 - x) = 0

33) Find s explicitly in terms of the other unknowns: 2s + 3p + st = q

34) Find s explicitly in terms of the other unknowns: 5stq + 6ps = 2 - 3s

35) Find s explicitly in terms of the other unknowns: pq = s(3t + 2)3t2 + 2p - q

36) Solve the equation: (1 - 2x)2 - 4(3 - x)2 = 5

37) Solve the equation: (3x - 1)2 - 9(1 + x)2 = 16

38) Solve the equation: (1 - 5x)2 - 25(x - 1)2 = 16

39) Your neighbor wants to carpet the rooms in her house. The widths of the rooms in her house are 1 yard lessthan the lengths. Write an equation which represents the area A of carpet needed for a room with length l.

40) You are driving an average of 60 mph and want to predict how far you will go in a given amount of time. Writean equation which represents the miles d you have gone in t hours.

41) A garage door companyʹs total monthly revenue from the sale of x garage doors is given by R = 925x and itstotal monthly costs are given by c = 575x + 2100. How many garage doors need to be sold each month to breakeven? In other words, when will revenue equal costs?

42) A comedy clubʹs nightly revenue from the sale of x tickets is given by r = 15x and its nightly costs are given by c = 1.25x + 495. How many tickets need to be sold each night to break even? In other words, when will revenueequal costs?

43) Sara and Jeff have agreed to pool their savings when they have saved the same amount of money. Sara cansave $40 a week but she must give her first $65 to her mom. Four weeks ago Jeff started saving $25 a week.When will they pool their savings? How much will they each have saved?

44) Eric and Paige have agreed to pool their savings when they have saved the same amount of money. Eric cansave $15 a week and will have an extra $80 when his brother pays him back in 3 weeks. Paige can save $20 aweek but wonʹt be able to start saving for 5 weeks. When will they pool their savings? How much will theyeach have saved?

45) Joe and Sue have agreed to pool their savings when they have saved the same amount of money. Joe can save$125 a week but he must use his first $375 to pay off his car. Sue has been saving $75 a week for 13 weeksalready. When will they pool their savings? How much will they each have saved?

46) Sally earns $15.00 per hour She has decided to automatically save one tenth of the money she earns after herweekly $10.00 Health Care Costs have been subtracted. She wants to save at least $50.00 each week. How manyhours must she work each week?

47) Jerry earns $26.00 per hour. He has decided his entertainment budget should be one eighth of the money heearns after his weekly $20.00 of automatic savings has been subtracted. He wants to spend at least $95.00 eachweek on entertainment. How many hours must he work each week?

48) Greg and Andrea want to buy a house, so they have decided to save one fifth of each of their salaries. Gregearns $15.00 per hour and receives an extra $5.00 a week because he declined company benefits, and Andreaearns $14.00 per hour plus benefits. They want to save at least $175.00 each week. How many hours must theyeach work each week?

49) S = 2πrh is the formula for the surface area S of the curved surface of a cylinder having radius r and height h.You have a rectangular sheet of wrapping paper which has a length l and a width w. What is the radius of thelargest-area cylinder having a height l that the wrapping paper will cover?

50) P = 2l + 2w is the formula for the perimeter P of a rectangle with length l and width w. If you have P linear feetof fencing material and are going to fence in an area for your dog which spans the length l of your yard, howwide can you make your fence?

51) C = 2πr is the formula for the circumference of a circle having a radius r. What is the radius of a bicycle wheelwhich has a circumference C?

52) A = πr2 is the formula for the area A of a circle with radius r. A circular tablecloth has an area A. What is itsradius?

53) S = 6l2 is the formula for the surface area S of a cube with sides of length l. You have wrapping paper withsurface area S. What is the length of the side of the largest cube the wrapping paper can cover?

54) Solve: 2x - 3x

= 3

55) Solve: x2 + 8x

- x = 3

56) Solve: 4x - 3x - 2

= 7x

57) Solve: 8x2 - 1

= 1x + 1

- 1x - 1

58) Solve: 1 + 3x = 2x + 6

59) Solve: x2 - 9 = x - 1

60) Solve: x - 1 = x - 1


61) Solve for x: 6x - 54x - 5

= 3x + 52x+ 5

A) 56

B) - 53

C) 2 D) 3 E) 0

62) Solve for x: 2xx - 4

+ 13 = 1

A) 2 B) -8 C) 8 D) -2 E) 0


63) Solve: 2x + 31 - 3x

= 4

64) Solve: 2x + 3 - 2x - 3 = 1

65) Solve: 4x2 + 5 - 1 = 2(x + 2)

66) Suppose the ratio of the number of hours a coffee shop is opened to the number of daily customers it gets isconstant. When it is opened 3 hours, the number of customers is 180 less than the maximum number ofcustomers. When it is opened 11 hours, the number of customers is 20 less than the maximum number ofcustomers. Write an equation describing this situation and find the maximum number of daily customers.

67) A boat with a speed of 12 mph travels 8 miles downstream in a current of cmiles an hour in the same time aboat going the same speed travels 4 miles upstream. Write an equation describing this situation and find thespeed of the current.

68) The time it takes a boat to travel a given distance downstream (with the current) can be calculated by dividingthe distance by the sum of the speed of the boat and the speed of the current. Write an equation whichcalculates the time t it takes a boat moving at a speed r against a current c to travel a distance d. Solve yourequation for r.

69) The time it takes an airplane to travel a given distance with a headwind (against the wind) can be calculated bydividing the distance by the difference of the speed of the airplane and the speed of the wind. Write anequation which calculates the time t it takes an airplane traveling at a speed r against a wind w to cover adistance d. Solve your equation for w.

70) The difference between the length of a ramp and the length of the horizontal distance it covers is 4 feet. Thesquare of the vertical distance it covers is 56 feet. What is the length of the ramp?

71) The difference between the length of a ramp and the length of the horizontal distance it covers is 1 foot. Thesquare of the vertical distance it covers is 9 feet. What is the length of the ramp?

72) The miles a person can see to the horizon from a point above the surface of Earth is 0.85 of the square root ofthe personʹs distance in feet above the surface. Talia is 13 feet higher and sees 0.85 farther than John. How highare Talia and John above the surface?

73) The miles a person can see to the horizon from a point above the surface of Earth is 0.85 of the square root ofthe personʹs distance in feet above the surface. Karen is 39 feet higher and sees 2.55 miles farther than Sharon.How high are Karen and Sharon above the surface?

74) The miles a person can see to the horizon from a point above the surface of Earth is 0.85 of the square root ofthe personʹs distance in feet above the surface. Sean is 65 feet higher and sees 4.25 miles farther than Craig.How high are Sean and Craig above the surface?

75) At a certain mall in Ohio, the sales tax is 7%. If the total receipt for a food processor was $160.50, what was theprice of the food processor?

76) What is the sales tax paid on an item whose total receipt was $100.75 and whose sales tax rate was 5.5%?

0.8 Quadratic Equations



1) Solve: x2 - 7x - 8 = 0

2) Solve: t2 + 8t + 7 = 0

3) Solve: 9x2 - 4 = 0

4) Solve: 2x2 - 9x + 4 = 0

5) Solve: 3y2 - 9y - 12 = 0

6) Solve: x2 = 5x

7) Solve: 4x2 - 4x + 1 = 0

8) Solve: x(4 - 2x) = -16

9) Solve: (x + 5)2 = 16

10) Solve: x2 - 3x = 0

11) Solve: 3x2 + x - 2 = 0

12) Solve: x2 - 6x + 9 = 0

13) Solve: (10 - 2x)(5 - x) = 50

14) Solve: y + 12y

+ y + 5y2

= 1

15) Solve: 3xx + 1

= x

16) Solve: 2x + 9x + 1

= 4

17) Solve: 2x - 15

x - 1 = 4

18) Solve: 6x2 - 1

= 3x + 1

+ 1

19) Solve: x6 + 6x = 2

20) Solve: x4 - 7x3 - 30x2 = 0

21) Solve: yy + 2

+ y + 4y - 3

= 7(2y - 1)y2 - y - 6

22) Solve: x + 2 = x - 4

23) Solve: 2x + 5 = x -5

24) Solve: 2x + 7 = x - 4

25) Solve: 2 x - 1 = 2x + 7

26) Solve: 3 = x2 - 8x

27) Solve: x4 - 2x2 + 1 = 0

28) Solve: x2 - 3x - 2 = 0

29) Solve: 2x2 + x - 4 = 0

30) Solve: 2x2 - 2x - 1 = 0

31) Solve: x22 - x = 1

3


32) The roots of (x - 1)(x + 2) = 10 are

A) 1 and -2 only

B) -1 and 2 only

C) -4 and 3 only

D) 8 and 11 only

E) -4 and 8 only

33) Find the sum of the roots of 3x2 + 7x - 6 = 0.

A) 0 B) 53

C) -7 D) - 73

E) 76

34) The roots of 13 + x - x = 7 are

A) -4 and -9 only

B) -4 and 9 only

C) -9 only

D) 4 only

E) -4 only

35) The roots of x + 2 = x - 4 are

A) 0 only B) 2 only C) 7 and 2 only D) 7 only E) -7 only

36) The equation 2x + x - 4 = 2 has exactly how many roots?

A) none B) one C) two D) three E) four

37) Solve for x: 1 - 4x - 4x2 = 0

A) 2 ± 2 2 B) -2 ± 2 2 C) 12

D) 12 ± 1 2

2E) - 1

2 ± 2

2

38) Which of the following is a root of 2x2 - 3x - 1 = 0?

A) 3 + 172

B) 17 - 34

C) 3 - 174

D) 3 - 172

E) 3 + 176


39) Solve the equation by factoring: 6x2 + 13x + 5 = 0

40) Solve the equation by factoring: 3x2 - 2x - 5 = 0

41) Solve the equation by factoring: x3 - 4x2 - 21x = 0

42) Solve the equation by using quadratic formula: 3x2 + 5x - 7 = 0

43) Solve the equation by using quadratic formula: 2p2 + p - 1 = 0

44) Solve the equation by using quadratic formula. Use a calculator and give your answer by rounding off to 2decimal places: .5x2 - 4.8x + 1.9 = 0

45) Solve the equation by using quadratic formula. Use a calculator and give your answer by rounding off to 2decimal places: 1.3x2 + 3.5x + 1.2 = 0

46) Determine whether the following equation has real roots. If it has real roots, find them, otherwise say no realroots. x - 1 + 2x + 1 = 1

47) Solve: 2 + 1x = 4x

48) Find the real roots of the equation: (x + 1)3 - 8 = 0

49) Solve: (2x + 1)2 - (3x + 2)2 + 5x2 + 8x + 3 = 0

50) Solve: (2x + 1)2 = 2(2x2 + 2x + 5)

51) Solve: 6x4 - 13x2 + 5 = 0

52) Solve: x4 - 8x2 + 15 = 0

53) A number squared is thirty-five more than twice the number. What is the number?

54) A number squared is four more than the opposite of three times the number. What is the number?

55) A number squared is six more than five times the number. What is the number?

56) The area of a rectangular table which has a length 1 foot more than its width is 20 square feet. What are thedimensions of the table?

57) The area of a rectangular swimming pool which has a length 15 meters more than its width is 250 squaremeters. What are the dimensions of the swimming pool?

58) The volume of a rectangular prism with a square base and height which is 16 times as long as its width is 4times its width. What are the dimensions of the rectangular prism?

59) The volume of a rectangular prism with a square base and height which is 27 times as long as its width is 3times its width. What are the dimensions of the rectangular prism?

60) The volume of a rectangular prism with a square base and height which is 116 times as long as its width is 4

times its width. What are the dimensions of the rectangular prism?

61) A number multiplied by itself is 7. What is the number?

62) You have been on a train for X hours traveling Xmiles per hour. It is 6 P.M. and you are 3249 miles from thetrain station. How many hours have you been traveling and how fast were you traveling?

63) Suppose the weekly revenue for a company is given by r = -2p2 + 400p where p is the price of their product.What is the price of their product if the weekly revenue is $18,750?

64) Suppose the height h in meters of fireworks fired straight upward from the ground is given by h = 24.5t - 4.9t2where t is in seconds. When will the fireworks be 20 meters off the ground?

65) Suppose the weekly revenue for a company is given by r = -3p2 + 60p where p is the price of their service. Whatis the price of their service if the revenue is $200?

66) Suppose the height h in feet of fireworks fired straight upward from the ground is given h = 160t - 16t2 where tis in seconds. When will the fireworks be 400 feet off the ground?

67) Suppose the height h in meters of fireworks fired straight upward from the ground is given by h = 24.5t - 4.9t2where t is in seconds. When will the fireworks be 30.625 meters off the ground?

68) Suppose the weekly revenue for a company is given by r = -3p2 + 60p where p is the price of their service. Whatis the price of their service if the weekly revenue is $300?

69) Suppose the weekly revenue for a company is given by r = -2p2 + 400p where p is the price of their product.What is the price of their product if the weekly revenue is $25,000?

70) Suppose the height h in meters of fireworks fired straight upward from the ground is given by h = 24.5t - 4.9t2where t is in seconds. When will the fireworks be 50 meters off the ground?

71) Suppose the weekly revenue for a company is given by r = -3p2 + 60p where p is the price of their service. Whatis the price of their service if the revenue is $400?

Ch. 0 Review of AlgebraAnswer Key

0.1 Sets of Real Numbers1) True2) True3) True4) False5) 4, -7, 0

6) 4, -7, 34, 0, - 0.2

7) D8) A

9) True, since .7 = 710

10) False11) infinitely many

0.2 Some Properties of Real Numbers1) distributive2) associative3) commutative4) associative5) A6) C7) -3

8) 13

9) distributive10) D11) 512) -813) 614) -1815) 816) 317) -218) 7x - 1419) -4 + x20) 0

21) 154x

22) 4

23) 4yx

24) 1

25) 56

26) 130

27) 5942

28) 32

29) xy4

30) 2xy

31) 032) B33) E34) A35) A36) C37) A

38) 13

39) - 23

40) 141) 10x - 642) 2x + 2

43) 2740

44) True

45) 353

46) - 116

0.3 Exponents and Radicals1) 6

2) 110

3) -4

4) 23

5) 27

6) 12

7) 27

8) 25

9) 16

10) 19

11) 164

12) 813) 2 514) y2

15) 432

16) 4x2

17) 16x29

18) 3x11

19) x12

20) 27x3

21) t3

22) 1z

23) x10

y5

24) x20y15

25) y11

26) x4

27) a8b4

81c12

28) x35

y12

29) 32y10

x15

30) 116x2

31) x3

32) y5

x5

33) x2

y2

34) x12z6

27y3

35) 4x2

y6

36) x5/6x

37) y4/5

xy2

38) 3 77

39) 83x2x

40)3207

41) 210

42) 5

43) 23x

5x44) C45) C46) C47) B48) E49) D50) C51) C52) A53) A54) E55) 34

56) 322

57) 432a13b18c858) 1

59) y2

x50/3

60) 2y3

x2

61) b15/4a

62)7a5

63) 2q3p2

64) 2

65)328

3a

2b

66) 2p2q2

67) 2x2y2

68) 2x2x

69) abb

70) ab23a2b

71) 3ab3 2a72) x5/4

73) x3/4y1/6

74)56st

0.4 Operations with Algebraic Expressions1) 4x - 2y - 32) 7x2 - 12x3) -2a - 14) 11x - 11y5) -2a + 2b - c6) 18x - 15

7) -4x2 + 5x - 198) -10x + 4y29) -14 + 2x10) 82 - 10x11) x2 + 5x + 412) x2 - 3x - 1013) 6y2 + 5y - 414) x2 + 4x - 2115) x2 + 10x + 2516) t2 - 917) 4x2 - 4x + 118) x2 + 6x + 819) y2 + 4y - 2120) z2 - 6z + 521) 9x2 + 24xy + 16y2

22) 4t2 - 2523) 6x2 - 10x - 424) x6 - 8125) x3 + 12x2 + 48x + 6426) 8x3 - 12x2 + 6x - 127) 4x3 + 8x2 + 4x28) 4x3 - 7x2 + 11x - 629) x4 - 1630) 3x + 231) 5x + 2032) 2x + 4y

33) x - 6 + 2x

34) 4x2y - x - 12y

35) x2

y2 + 4y2 - 3

x2y

36) x - 1 - 6x - 2

37) 2x2 - x + 3 - 62x + 1

38) D39) E40) C41) C42) B43) C44) D45) C46) A47) E48) C49) D50) C

51) B52) A53) D54) B55) E56) 2x2y + 5xy2 - 3x + 12y - 11xy

57) 2a2b + 2a - 165b

58) - 45x2y - 1

3xy2 - 19x + 12y + 11xy

59) 107a3bc - 6

7ab2 + 6

5a2b + 12

5a + 6

5b

60) 14a3 + 14a2b - 56ab + 56b2

61) a2 - 3ab - 2b2

62) 5a2 + 5ab - 15b2 + 15a2 b63) t2 - 4s2

64) a2 - b2 - c2 + 2bc

65) 121x2 - 4

21y2

66) 2a3 + a2b - 2ab2 - b3

67) x4 - 2x2 + 168) b2

69) quotient = x2 + 2x + 4; remainder = 570) quotient = 2x + 7; remainder = 19

71) quotient = 12x + 5

4; remainder = 15

472) quotient = x - 1; remainder = 9x + 8

73) quotient = 12x + 3

2 ; remainder = 11

2x + 17

2

74) a3 - 3ab2 + 2b3

75) 8a2 - 36a2b + 54ab2 - 27b3

76) a3

0.5 Factoring1) 5(x - 1)2) 3a(x + 3y)3) 2xy2(2y + 3 - y2)4) x2/5y3(x - 35y)5) (x + 6)(x - 6)6) (x + 1)(x + 3)7) (2y + 5)(2y - 5)8) (x - 2)(x - 8)9) (t - 9)(t + 1)10) (x + 3)2

11) 9(2x + 5)212) (x + 4)(x -3)13) (2y + 1)(y +3)14) (2z - 5)(3z + 1)15) (4x - 3)(x + 2)16) (4t +1)217) (x - 4)(x + 3)(x - 3)

18) (y + 2)(y - 2)(y + 1)219) 2(x + 2)(x -2)20) x(x + 2)(x +3)21) 3x2(x + 1)222) (x + 2)(2x + 7)23) 8(x + 3)(x - 5)3

24) 2(x - 2)(x2 + 2x + 4)25) (x2 - 3y)(x4 + 3x2y + 9y2)26) (x2 + 1)(x + 1)(x - 1)27) (x2 + 9)(x + 2)(x - 2)28) D29) B30) B31) E32) D33) A34) C35) C36) B37) A38) (a - 2b)(a2 + 2ab + 4b2)39) (p - 2)(p + 2)(p2 + 4)40) x(x - 2)(x2 + 2x + 4)41) -5x(3x - 5)42) 2(t + 3)(t + 1)43) (2x + 5)(2x - 5)44) -(x - 1)(x + 3)45) (2x + 3)(x + 1)46) (a - 3b)(a + 3b)(a2 + b2)47) xy(x + 11y)48) (a + b - c) a2 - a(b - c) + (b - c)2

49) (x-1 + 10)(x-1 - 2)0.6 Fractions

1) 2x

2) z

3) - 12(x - 2)

4) x - 2x - 4

5) x6y

6) 6yx

7) 827xy

8) 4z2

9) x(x + 2)2(x - 2)

10) 2(x - 1)(x + 2)(x + 1)

11) x(x - 3)

12) 4 - x22x

13) x + 3

14) 2x2 + 3x + 12(2x - 1)(x + 3)

15) 7y - 8x + 3xyxy

16) 4 x + 7x + 3

17) - x(2x + 3)3(x + 3)(x - 3)

18) 2x2 + 7x + 14(x + 1)2(x + 4)

19) 2x2 + 5x -1x2(x + 1)(x - 1)

20) - x5

21) 1 - xx - 4

22) 7(x + 1)(x - 1)

23) 3x - 24x

24) y(x + 1)x(2y - 1)

25) a2 + b2

a2 - b2

26) 211

27) 2x(3 - 2x)

28) 2(x + 2)2

29) 11 + 4x

30) xx - 1

31) 3 + 27

32) 15 - 32

33) B34) E35) B36) A

37) D38) C39) B40) E41) E42) B43) C44) D

45) a2 + 2ab + 4b2a - 3b

46) x - 2

47) 2(x + 1)x2

48) a2 + 5ab +3b2

49) (a + b)2a + 2b

50) (a + b)(3a - b)(a - b)(2a + b)

51) 5x212

52) xy + 1xy - 1

53) 1

54) 3x + 22x + 1

55) 32x - 112(x - 2)

56) 22x + 2h + 2x

57) 3x2 + 4

x2 + 1

58) 2x3 + x2 + 2x - 1x4 - 1

59) 4 + 4 x + x4 - x

60) x2 + 13x + 102x2 + 2x

0.7 Equations, in Particular Linear Equations1) x = 21

2

2) y = - 710

3) x = - 12

4) q = 34

5) x = 452

6) x = 3

7) z = 199

8) x = 32

9) x = 152

10) t = 2

11) x = 74

12) x = 78

13) x = 1914) x = -115) No solution

16) x = 2a - 3ba

17) x = 2b - 3a - b

18) L = katTh

19) t = S -PPr

20) x = - 12

21) False22) True23) 25° C24) A25) C26) D27) E28) D29) x = 3.4530) x = 2

31) x = 2513

32) x = 747

33) s = q - 3p2 + t

34) s = 25tq + 6p + 3

35) s = pq(3t2 + 2p - q)3t + 2

36) x = 237) x = -138) x = 139) A = l(l - 1) = l2 - l40) d = 60t41) 6 garage doors

42) 36 tickets43) 11 weeks: $37544) 36 weeks; $62045) 27 weeks; $300046) 34 hours47) 30 hours48) 30 hours

49) r = w2π

50) w = P - 2l2

51) r = C2π

52) r = Aπ

53) l = S6

54) x = -3

55) x = 83

56) x = 157) no solution58) x = 559) x = 560) x = 161) E62) D

63) x = 114

64) x = 378

65) x = - 34

66) 3x - 180

= 11x - 20

; 240

67) 812 + c

= 412 - c

; 4 mph

68) t = dr + c

; r = dt - c

69) t = dr - w

; w = r - dt

70) 9 feet71) 5 feet72) John is 36 feet above the surface; Talia is 49 feet above the surface.73) Sharon is 25 feet above the surface; Karen is 64 feet above the surface.74) Craig is 16 feet above the surface; Sean is 81 feet above the surface.75) $150.0076) $95.50

0.8 Quadratic Equations1) x = -1, 82) t = -7, -1

3) x = ± 23

4) x = 4, 12

5) y = 4, -16) x = 0, 5

7) x = 12

8) x = -2, 49) x = -1, -910) x = 0, 3

11) x = -1, 23

12) x = 313) x = 0, 1014) y = 5, -215) x = 0, 2

16) x = 2, - 14

17) x = -2, - 14

18) x = -5, 219) x = 620) x = -3, 0, 10

21) y = 52

22) x = 723) x = 1024) x = 925) x = 926) x = 9, -127) x = ±1

28) x = 3 ± 172

29) x = -1 ± 334

30) x = 1 ± 32

31) x = 1± 153

32) C33) D34) E35) D36) A37) E38) C

39) x = - 12; - 5

3

40) x = -1; 53

41) x = 0, -3, 7

42) x = -5 ± 1096

43) p = -2, 12

44) x = .41; 9.1945) x = 0.4; -2.2946) no real roots

47) 1 ± 54

48) x = 149) all real numbers50) no solution

51) x = ± 12; ± 5

3

52) x = ± 3; ± 553) The number is -5 or 7.54) The number is -4 or 1.55) The number is -1 or 6.56) 4 feet by 5 feet57) 10 meters by 25 meters

58) 12 × 1

2 × 8

59) 13 × 1

3 × 9

60) 8 × 8 × 12

61) ± 762) 57 miles per hour for 57 hours.63) The price is $75 or $125.64) about 1 second and about 4 seconds65) The price is $4.23 or $15.77.66) 5 seconds67) 2.5 seconds68) The price is $10.69) There is no price that would give a weekly revenue of $25,000.70) never71) There is no price that would give a weekly revenue of $400.

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