Chapter 5 A census was taken to determine the median annual income

Provide an appropriate response.

55)

Write a polynomial in descending powers of x that represents the area of the entire figure.

2x 3

2x + 1

3

A)

4x2+12x +11

B)

8x +14

C)

16x2+56x +48

D)

4x2+14x +12

Simplify the exponential expression.

56)

x–8·x5

56)

A)

1

x13

B)

1

x3

C)

x3

D)

x13

Find the product.

57)

x(x – 5)

A)

x2– 5x

B)

–4x2

C)

2x – 5

D)

x2– 5

58)

(x2–3y2)2

58)

A)

x4–3x2y2+9y4

B)

x4–6x2y2+9y4

C)

x4+9y4

D)

x4–9y4

Use a vertical format to add the polynomials.

59)

9x4+ 2x3

6x4+ 7x3

59)

A)

24x7

B)

15x4+ 9x3

C)

15x8+ 9x6

D)

24x14

Write the number in scientific notation.

60)

1532

A)

1.532 x 103

B)

1.532 x 101

C)

1.532 x 10–3

D)

1.532 x 104

Find the area of the shaded region. Write the answer as a polynomial in descending powers of x.

61)

(4x – 10)

(7x + 10)

A)

28x2– 30x + 100

B)

28x2– 30x – 100

C)

28x2–70x – 100

D)

28x2+110x – 100

Write the expression with positive exponents only. Then simplify, if possible.

62)

1

3x–4

62)

A)

x4

3

B)

3

x4

C)

3x4

D)

–1

12x

Solve.

63)

The bar graph shows the median annual income for residents of a selected region of the United

States, by level of education. The given polynomial models describe the median annual income

for men, M, and for women, W, who have completed x years of education.

M = – 23x3+ 1170x2– 13,808x + 72,566

W = 8x3– 56x2+ 511x + 14,763

Find a mathematical model for M – W and use it to calculate the difference in the median annual

income between men and women with 8 years of education. Does the model underestimate or

overestimate the actual difference?

A)

$4533; underestimates

B)

$1325; underestimates

C)

$5843; overestimates

D)

$14,019; overestimates

Find the product.

64)

12x7(–6x5+ 10x4+ 2)

64)

A)

–72x12 + 10x4+ 2

B)

–72x12 + 120x11 + 24x7

C)

–72x5+ 120x4+ 24

D)

–72x12 + 120x11

20

Use a vertical format to subtract the polynomials.

65)

4x4–4x3+7x2

–( –x3–9x2+x– 14)

65)

A)

4x4–5x3– 2x2–x+ 14

B)

4x4–3x3– 2x2+x– 14

C)

4x4–3x3+16x2–x+ 14

D)

4x4–5x3+16x2+x– 14

Use synthetic division to divide.

66)

(x2– 3x – 18) ÷ (x – 6)

66)

A)

x + 3

B)

x – 18

C)

x – 6

D)

x – 3

Write the expression with positive exponents only. Then simplify, if possible.

67)

1

3–2

67)

A)

9

B)

2

3

C)

1

–6

D)

1

9

Divide the polynomial by the monomial.

68)

40x8– 12x6+ 8x2

4x2

68)

A)

10x8– 3x6+ 2x2

B)

10x6– 3x4+ 2

C)

40x6– 12x4+ 8

D)

10x6+ 3x4– 2

Solve.

69)

A census was taken to determine the median annual income for residents of a selected region of

the United States, by level of education. The given polynomial models describe the median

annual income for men, M, and for women, W, who have completed x years of education. Shown

in a rectangular coordinate system are the graphs of the polynomial models. Identify the median

annual income for a woman with 13 years of education as a point on the appropriate graph.

M = 224x2– 1266x + 20,106

W = 287x2– 4030x + 33,761

A)

(13, 41,504)

B)

(13, 56,696)

C)

(13, 78,234)

D)

(13, 29,874)

Divide the polynomial by the monomial.

70)

12x7– 40x5

4x3

70)

A)

3x4– 40x5

B)

–7x9

C)

12x7– 10x2

D)

3x4– 10x2

Simplify the expression using the quotients–to–powers rule.

71)

3x3

y2

4

71)

A)

81x12

y8

B)

3x12

y8

C)

81x12

y2

D)

82x7

y6

Write the number in scientific notation.

72)

810,000

A)

8.1 x 10–6

B)

8.1 x 105

C)

8.1 x 106

D)

8.1 x 10–5

Find the product.

73)

6xy(2x +8y)

A)

60x2y2

B)

60x2y

C)

8x2y +14xy2

D)

12x2y +48xy2

Write the expression with positive exponents only. Then simplify, if possible.

74)

1

2–3

74)

A)

1

8

B)

8

C)

3

2

D)

1

–6

Find the product.

75)

(6xy2–5y)(6xy2+5y)

75)

A)

36x2y4+25y2

B)

36x2y4–60xy3–25y2

C)

36xy2–25y

D)

36x2y4–25y2

Multiply the monomials.

76)

–1

8x9–1

9x8

76)

A)

–1

72 x72

B)

–1

72 x17

C)

1

72 x72

D)

1

72 x17

Simplify the expression using the quotients–to–powers rule.

77)

2

y2

4

77)

A)

16

y2

B)

17

y6

C)

2

y8

D)

16

y8

Write the number in scientific notation.

78)

473.91

A)

4.7391 x 103

B)

4.7391 x 10–3

C)

4.7391 x 102

D)

4.7391 x 10–2

Add or subtract as indicated.

79)

Add:

3x2–xy –y2

x2+6xy +10y2

A)

2x2– 7xy – 11y2

B)

4x2+7xy +11y2

C)

3x2+6xy +10y2

D)

4x2+5xy +9y2

Multiply using the rule for finding the product of the sum and difference of two terms.

80)

3x +1

33x –1

3

80)

A)

9x2–2

3x +1

9

B)

9x2–2

3x –1

9

C)

9x2–2

3

D)

9x2–1

9

Use the zero–exponent rule to simplify the expression.

81)

(–13)0

81)

A)

0

B)

–13

C)

1

D)

–1

Multiply using the rule for finding the product of the sum and difference of two terms.

82)

(7 + r)(7– r)

A)

49 + 14r –r2

B)

49 – 14r –r2

C)

14 –r2

D)

49 –r2

25

Multiply by using the rule for the square of a binomial.

83)

11x –1

11

2

83)

A)

121x2–2

11 x +1

121

B)

121x2– 2x –1

121

C)

121x2–1

121

D)

121x2– 2x +1

121

Divide the polynomial by the monomial.

84)

36x9y8– 72x2y5– 45x5y2

9x2y2

84)

A)

36x7y6– 72y3– 45x3

B)

4x7y8– 8y5– 5x3y2

C)

4x7y6– 8y3– 5x3

D)

4x9y8– 8x2y5– 5x5y2

Find the product.

85)

–7x(x – 8)

A)

–7x2+ 56x

B)

x2+ 56x

C)

49x2

D)

–7x2– 8x

Use the FOIL method to find the product. Express the product in descending powers of the variable.

86)

(6x + 2)(x + 9)

A)

6x2+ 56x + 18

B)

6x2+ 18x + 56

C)

6x2+ 54x + 18

D)

6x2+ 56x + 56

Solve.

87)

A particle is observed moving at 5.39 ×10–5 meters per second. Find the distance the particle

would travel in 2.58 ×10–6 seconds.

87)

A)

1.39 ×10–9 meters

B)

1.39 ×10–10 meters

C)

0.14 ×10–10 meters

D)

1.39 ×10–11 meters

Multiply the expression using the product rule.

88)

48·46

88)

A)

1614

B)

1648

C)

448

D)

414

Rewrite the number in the statement in scientific notation.

89)

An music album sells 97,800,000 copies.

A)

9.78 ×106

B)

9.78 ×107

C)

9.78 ×105

D)

9.78 ×10–6

Multiply by using the rule for the square of a binomial.

90)

9x +1

9

2

90)

A)

81x2+ x +1

81

B)

81x2+ 2x +1

81

C)

81x2+1

81

D)

81x2+2

9x +1

81

27

Solve.

91)

A census was taken to determine the median annual income for residents of a selected region of

the United States, by level of education. The given polynomial models describe the median

annual income for men, M, and for women, W, who have completed x years of education. Shown

in a rectangular coordinate system are the graphs of the polynomial models. Identify the median

annual income for a man with 10 years of education as a point on the appropriate graph.

M = 224x2– 1266x + 20,106

W = 287x2– 4030x + 33,761

A)

(10, 58,431)

B)

(10, 29,846)

C)

(10, 22,161)

D)

(10, 41,240)

Multiply the expression using the product rule.

92)

y10 ·y2

92)

A)

2y20

B)

y20

C)

y12

D)

2y12

Write the number in scientific notation.

93)

0.000061818

A)

6.1818 x 104

B)

6.1818 x 10–5

C)

6.1818 x 10–4

D)

6.1818 x 105

Simplify the exponential expression.

94)

(x3)3

x15

94)

A)

1

x24

B)

x6

C)

1

x6

D)

1

x9

Add or subtract as indicated.

95)

(30x2y2+ 9y4) – (–4x4– 15x2y2+ 9y4)

95)

A)

4x4+ 45x2y2

B)

–4x4+ 15x2y2+ 18y4

C)

4x4+ 45x2y2– 18y4

D)

49x6y4

Find the product.

96)

1

4x – 9 1

3x + 8

96)

A)

1

12 x2– 12x – 12

B)

1

12 x2– 1x – 72

C)

1

12 x2– 36x – 72

D)

–1

12 x2– 1x – 72

97)

9xy2(3x2y3+6xy)

97)

A)

27x2y6+54xy2

B)

27x3y5+54x2y3

C)

12x2y6+15xy2

D)

12x3y5+15x2y3

Add or subtract as indicated.

98)

Subtract:

(2x5+ 2x3y – 8y2)

– (6x5– 2x3y + 3y2)

A)

–11x9y3

B)

–4x5+ 4x3y – 11y2

C)

–4x5+ 8x3y – 5y2

D)

–4x5+ 4x3y – 5y2

Use a vertical format to find the product.

99)

5z3+7z2+4z +4

4z +7

99)

A)

63z4+63z3+77z2+28z

B)

20z4+35z3+77z2+44z+44

C)

63z4+77z3+44z2+44z

D)

20z4+63z3+65z2+44z+28

Simplify the expression using the quotients–to–powers rule.

100)

a

5

2

100)

A)

a2

10

B)

a

25

C)

a2

25

D)

a

10

Divide and check the answer.

101)

18x6–30x4+6x2

6x

101)

A)

18x5–30x3+ 1

B)

3x6– 5x4+x2

C)

3x5– 5x3+ x

D)

3x7– 5x5+ x