Chapter 4
Polynomials: Operations
Exercise Set 4.1
2. 4·4·4
10. 17 ·x·x
20. 4
5
26. ab1=a·b1=ab
36. z5+5=(−2)5+5=−32+5=−27
42. A=s2= (24 m)2= 576 m2
50. 25=32
52. t7
62. b−7
70. x13
80. 1
y13
84. a8c11
86. m6n8
100. x−9
108. −1
82=−1
81
8=−1
64
110. Solve: (x+ 24) + x+2(x+ 24) = 180
112. Solve: 10l<25
118. Let y1=(x−1)2and y2=x2−2x+ 1. A graph of the
10. a28
16. x2y2
22. 4x6
38. (−8x3y−2)3=(−8)3x9y−6=−512x9
y6
54. 4.900,000,000,000.
56. 1.68,000,000,000,000.
62. 0.0000001.
64. 0.00000002.8
66. 1.5,000,000,000.
68. Positive exponent, so the answer is a large number.
70. Negative exponent, so the answer is a small number.
72. Positive exponent, so the answer is a large number.
76. (3.9×108)(8.4×10−3)=32.76 ×105=
84. (1.5×10−3)÷(1.6×10−6)=0.9375 ×103=
5×10−24
90. 150 million = 1.5×108and 1 million = 106.
94. 50 gigabytes = 50 ×109=5.0×1010 bytes
96. 1.5×10−6
2
y 4
x 4
100.
104.
106.
112. 5x−2
3y−2z0
=1
118. False; let x=3,y= 4, and m=2:
120. False; Let x= 3 and m=2:
122. False; let x= 4 and m=2:
Exercise Set 4.3
RC2. (f)
2. −8x+1=−8·4+1=−32+1=−31;
8. 8−1
4x=8−1
4(−2) = 8 + 1
2=17
2;
10. 5x+6−x2=5(−2)+6−(−2)2=
−2x3+5x2−4x+3=
Exercise Set 4.3 79
18. When x=−1, y=0.
20. a) N=1.24(30) + 28.4=65.6 million people
5x5,−x3,6
32. Monomial
Term Coefficient Degree of Degree of
−1
2x4−1
24
66. 4x4+5
72. 1
6x3+2x−12
86. −4x3−6x
98. 5x4+0x3+0x2−7x+2
104. −5
8+1
4=−5
8+2
8=−3
8
110. −1
22
3=−1·2/
2/ ·3=−1
3
122. Graph y=6x3−6x. Then use “value” from the CALC
124. Graph y=−0.001x3+0.1x2. Then use “value” from the
Exercise Set 4.4
RC2. True
6. 3x3−4x2
14. 2
15x9−2
5x5+1
4x4+1
4x2+15
2
28. 2x−4
38. −x3+6x2
46. 0.1x4−0.9
54.
2y+3
7
2y
7y
The perimeter is the sum of the lengths of the sides. The
sum of the lengths is found as follows:
58.
t2+8t+ 15.
60. x10
x+10
✛ ✲
x+8
❄
Chapter 4 Mid-Chapter Review 81
Another way to express the area is to find an expression
Area
of A+Area
of B+Area
of C+Area
of D
This can also be expressed as
62.
m
m
✻
64. The circle has radius rand the square has side 7.
66. 5x−7x=38
68. 5x−4=26−x
72. 8(5x+ 2) = 7(6x−3)
74. 2(x−4) >5(x−3)+7
76. Surface area = 2 ·9·x+2·9·x+2·x·x=
14a+56+8a=22a+56
80. (3x2−4x+6)−(−2x2+4)+(−5x−3)
82. (−4+x2+2x3)−(−6−x+3x3)−(−x2−5x3)
Chapter 4 Mid-Chapter Review
6. 3y4−y2+11−(y4−4y2+5)
11. 53·54=5
3+4 =5
7
8−4=7
4
17. w5
21. a4
=a4·6
0.00012 = 1.2×10−4
25. 3.6×10−5
27. (3 ×106)(2 ×10−3)=(3×2) ×(106×10−3)=
29. −3x+7=−3(−3)+7=9+7=16;
x3−2x+5=2
3−2·2+5=8−4+5=9
35. x−9 has two terms. It is a binomial.
42. Let s= the length of a side of the smaller square. Then
3s= the length of a side of the larger square. The area of
47. Yes; consider the following.
Exercise Set 4.5
x ⫹ 2
4x24
4
16. 12x2−18x
18. 3x2+3x
26. 4y7−24y6
28. x2+7x+10
34. x2−10x+21
40. 18+12x+2x2
46. x2−12x+36
56.
60.
62. (x2+x−2)(x+2)
64. (3x−1)(4x2−2x−1)
66. (3y2−3)(y2+6y+1)
68. (x3−x2)(x3−x2+x)
70. (−4x3+5x2−2)(5x2+1)
72. 1−x+x2
1−x+x2
74. 3a2−5a+2
2a2−3a+4
x
1
78. (x+ 2)(x3+5x2+9x+3)
80. x+1
36x3−12x2−5x+1
2
6x+1
6
82. 5−2[3 −4(8 −2)]=5−2[3 −4·6]
84. 10 −2+(−6)2÷3·2
86. 4(4x−6y+9)
88. 100(x−y+10a)
90. The shaded area is the area of the large rectangle less the
known areas.
94.
The interior dimensions of the open box are x−2cmby
96. (x+5)
2−(x−3)2
=(x+ 5)(x+5)−(x−3)(x−3)
98. Left to the student
Exercise Set 4.6
RC6. The product of the sum and the difference of the same
16. q2+3
2q+9
16
Exercise Set 4.6 85
26. −3x2−5x−2
34. x2+11
46. 9x8−4
74. 9p4−6p3+p2
92. 3
104. 3(x−2) = 5(2x+7)
106. 3x−2y=12
108. 3a−5d=4
112. (a−3)2(a+3)
2
=[(a−3)(a+ 3)]2
86 Chapter 4: Polynomials: Operations
118. a)
A✲✛
b)
A+B
✻
A
✛ ✲
c) Area in part (a) – area in part (b)
120. Enter y1=(x−2)2and y2=x2−4x−4. Then compare
122. Enter y1=(x−3)(x+ 2) and y2=x2−x−6. Then
Exercise Set 4.7
10. h=h0+vt−4.9t2=32+10·3−4.9(3)2=17.9m
22. y−7
32. 8ab +6a−9b
42. a2+2ab +b2
a3+a2b−ab2−b3
m3n−m2n2+mn3
m4+m2n2+n4
Exercise Set 4.8 87
58. (y−a)2=y2−2ya +a2
66. −3x(x+8y)2=−3x(x2+16xy +64y2)=
74. p6−25q2
=a2−(b+c)2
=9x2+12x+4−25y2
84. 2x2−7y+4
86. III
92. −[−(−3)] = −3
96. a2−4b2
100. Replace twith 2 and multiply.
P(1 + r)2
Exercise Set 4.8
2. −2u
4. −8x5
2a2+1
6a−1
12. 50x4−7x3+x