12.4.10: Chapter 10
- Page ID
- 119031
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Try It
- ⓐ monomial
- ⓑ polynomial
- ⓒ trinomial
- ⓓ binomial
- ⓔ monomial
- ⓐ binomial
- ⓑ trinomial
- ⓒ polynomial
- ⓓ monomial
- ⓒ monomial
- ⓐ 1
- ⓑ 1
- ⓒ 4
- ⓓ 2
- ⓔ 0
- ⓐ 0
- ⓑ 2
- ⓒ 4
- ⓓ 5
- ⓔ 3
17x2
−3y2
14n
−2a3
−2x2 + 3y2
−2a2 + b2
4x2 − 8x + 10
11y2 + 9y − 5
3y2 + 3y + 3
3u2 − u + 2
4n2 + 12n
5a2 + 8a + 8
- ⓐ 13
- ⓑ 3
- ⓐ 114
- ⓑ −2
4 feet
20 feet
- ⓐ 64
- ⓑ 11
- ⓐ 81
- ⓐ 21
- ⓐ
- ⓑ
- ⓐ
- ⓑ
- ⓐ 16
- ⓑ −16
- ⓐ 64
- ⓑ −64
x 15
x 16
p 10
m 8
610
915
y 43
z 39
x 21
y 15
- ⓐ x 28
- ⓑ 732
- ⓐ x 54
- ⓑ 842
196x2
144a2
256x4y4
216x3y3
x 40
y 42
−512x12y21
81a20b24
98n14
48m5
64u18v22
675x7y18
−56x11
54y9
12m5n6
12p11q8
6x + 48
2y + 24
y2 − 9y
p2 − 13p
8x2 + 24xy
18r2 + 3rs
−32y3 − 20y2 + 36y
−54x3 − 6x2 + 6x
12x4 − 9x3 + 27x2
24y4 − 16y3 − 32y2
xp + 8p
ap + 4p
x2 + 17x + 72
a2 + 9a + 20
20x2 + 51x + 27
80m2 + 142m + 63
56y2 − 13y − 3
15x2 − 14x − 16
x2 − xy + 5x − 5y
x2 − x + 2xy − 2y
x2 + 15x + 56
y2 + 16y + 28
y2 + 5y − 24
q2 + q − 20
20a2 + 37a − 18
49x2 − 28x − 32
12x2 − 60x − xy + 5y
12a2 − 54a − 2ab + 9b
12m2 − 55m + 63
42n2 − 47n + 10
y3 − 8y2 + 9y − 2
3x3 + 2x2 − 3x + 10
y3 − 8y2 + 9y − 2
3x3 + 2x2 − 3x + 10
- ⓐ x3
- ⓑ 79
- ⓐ y 6
- ⓑ 88
- ⓐ
- ⓑ
- ⓐ
- ⓑ
- ⓐ
- ⓑ
- ⓐ
- ⓑ
- ⓐ 1
- ⓑ 1
- ⓐ 1
- ⓑ 1
1
1
- ⓐ 1
- ⓑ 7x2
- ⓐ −23x2
- ⓑ 1
- ⓐ
- ⓑ
- ⓒ
- ⓐ
- ⓑ
- ⓒ
a 11
b 19
k 2
f 12
9x5
7x4
16y3
2xy2
−4ab5
- ⓐ
- ⓑ
- ⓐ
- ⓑ
- ⓐ
- ⓑ
- ⓐ
- ⓑ
- ⓐ
- ⓑ
- ⓐ
- ⓑ
- ⓐ
- ⓑ
- ⓒ
- ⓐ
- ⓑ
- ⓒ
- ⓐ
- ⓑ
- ⓒ
- ⓐ
- ⓑ
- ⓒ
x 11
y 13
9.6 × 104
4.83 × 104
7.8 × 10−3
1.29 × 10−2
1,300
92,500
0.00012
0.075
0.06
0.009
400,000
20,000
18
16
7
11
8x2
9y3
3x
5m2
4(x + 3)
6(a + 4)
9(a + 1)
11(x + 1)
11(x − 4)
13(y − 4)
4(y2 + 2y + 3)
6(x2 + 7x − 2)
x(9x + 7)
a(5a − 12)
2x2(x + 6)
3y2(2y − 5)
9y(2y + 7)
8k(4k + 7)
6y(3y2 − y − 4)
4x(4x2 + 2x − 3)
−5(y + 7)
−8(2z + 7)
−7a(a − 3)
−x(6x − 1)
Section 10.1 Exercises
binomial
trinomial
polynomial
monomial
5
1
0
15x2
−8u
5a + 7b
−4a −3b
16x
−17x6
12y2 + 4y + 8
−3x2 + 17x − 1
4a2 − 7a − 11
4m2 − 10m + 2
11z + 8
12s2 − 16s + 9
2p3 + p2 + 9p + 10
x2 + 3x + 4
11w − 66
- ⓐ 187
- ⓑ 40
- ⓒ 2
- ⓐ −104
- ⓑ 4
- ⓒ 40
19 feet
10 mpg
Answers will vary.
Section 10.2 Exercises
1,024
0.008
625
−625
−10,000
−0.25
x 9
a 5
314
z 6
x a+2
y a+b
u 8
y 20
1012
x 90
x 2y
5xy
25a2
−216m3
16r2s2
256x4y4z4
x 14
a 36
45x3
200a5
8m18
1,000x6y3
16a12b8
1,024a10
25,000p24
x 18 y 18
144m8n22
−60x6
72u7
4r11
36a5b7
8x2y5
1,679,616
Answers will vary.
Answers will vary.
Section 10.3 Exercises
4x + 40
15r − 360
−3m − 33
−8z + 40
u2 + 5u
n3 − 3n2
12x2 − 120x
−27a2 − 45a
24x2 + 6xy
55p2 − 25pq
3v2 + 30v + 75
8n3 − 8n2 + 2n
−8y3 − 16y2 + 120y
5q5 − 10q4 + 30q3
−12z4 − 48z3 + 4z2
2y2 − 9y
8w − 48
x2 + 10x + 24
n2 + 9n − 36
y2 + 11y + 24
a2 + 22a + 96
u2 − 14u + 45
z2 − 32z + 220
x2 + 3x − 28
v2 + 7v − 60
6n2 + 11n + 5
20m2 − 88m − 9
16c2 − 1
15u2 − 82u + 112
2a2 + 5ab + 3b2
5x2 − 20x − xy + 4y
u3 + 7u2 + 14u + 8
3a3 + 31a2 + 5a − 50
y3 − 16y2 + 69y − 54
2x3 − 9x2 − 17x − 6
- ⓐ 195
- ⓑ 195
- ⓒ Answers will vary.
Answers will vary.
Section 10.4 Exercises
46
x 9
r 4
1
1
−1
- ⓐ 1
- ⓑ 10
- ⓐ 1
- ⓑ −27x5
- ⓐ 1
- ⓑ 15
7
x 3
u 2
1
a 14
y 3
1
3x8
8b6
2x
5u4v3
- ⓐ
- ⓑ
- ⓒ
- ⓓ
- ⓐ
- ⓑ
- ⓐ
- ⓑ
1,000,000
Answers will vary.
Answers will vary.
Section 10.5 Exercises
- ⓐ
- ⓑ
- ⓐ
- ⓑ
- ⓐ
- ⓑ
- ⓐ
- ⓑ
- ⓐ
- ⓑ
- ⓒ
- ⓐ
- ⓑ
- ⓒ
r 3
m 6
b 8
m 7
p 3
2.8 × 105
1.29 × 106
4.1 × 10−2
1.03 × 10−5
6.85 × 109
5.7 × 10−9
830
16,000,000,000
0.028
0.0000000615
$15,000,000,000,000
0.00001
0.003
0.00000735
20,000,000
50,000,000
- ⓐ 1.25 × 10−4
- ⓐ 8,000
11,441,304,000
Answers will vary.
Section 10.6 Exercises
15
25
4
5
3x
12p3
2a
10y
5x3
7b2
5(y + 3)
4(b − 5)
7(x − 1)
3(n2 + 7n + 4)
6(q2 + 5q + 7)
c(9c + 22)
x(17x + 7)
q(4q + 7)
3r(r + 9)
10u(3u − 1)
b(a + 8)
11y(5 − y3)
15c2(3c − 1)
6c(c2 − d2)
24x2(2x + 3)
18a3(8a3 + 5)
10(y2 + 5y + 4)
12(u2 − 3u − 9)
5p2(p2 − 4p − 3)
8c3(c2 + 5c − 7)
−7(p + 12)
−6b(3b + 11)
−8a2(a − 4)
−9b3(b2 − 7)
−4(4t2 − 20t − 1)
Answers will vary.
Review Exercises
trinomial
binomial
2
0
15p
−3n5
10a2 + 4a − 1
6y2 − 3y + 3
8q3 + q2 + 6q − 29
995
2,955
−163
64 feet
216
0.25
p 13
a 6
y 12
310
64n2
256a8b8
27a15
x 21
−54p5
56x3y11
70 − 7x
−625y4 + 5y
a2 + 7a + 10
6x2 − 19x − 7
n2 + 9n + 8
5u2 + 37u − 24
p2 + 11p + 28
27c2 − 3c − 4
x3 − 2x2 − 24x − 21
m3 − m2 − 72m − 180
26 or 64
1
1
a 2
9p9
x 6
k 6
b 10
5.3 × 106
9.7 × 10−2 millimeter
29,000
0.375
6,000
30,000,000,000
5
4x2
8(2u − 3)
6p(p + 1)
−9a3(a2 + 1)
5(y2 − 11y + 9)