Chapter 5 Review Exercises
10.
()
2
2
7 9 2
427
xx
xx
−+
−−−
11.
()
32
32
5 6 9 14
5311 3
xx x
xx x
−−+
−− + − +
12.
()
()
2
2
2
3(,)
3(3)3123,12
2(2)372,7
xyx xy
y
y
=+
−=−+= −
−=−+=−
13.
()
()
2
2
2
1(,)
21(2)32,3
31(3)83,8
xyx xy
y
y
=−
=− =− −
=− =− −
14.
20 3 20 3 23
xx x x
+
⋅= =
15.
58 158 158 14
yy y y y y y y
++
⋅⋅=⋅⋅= =
16.
()
5
20 20 5 100
xxx
⋅
==
19.
()
()
()
()
5 10 5 10 50xx xx x=⋅ ⋅ =
20.
()()
74 11
12 3 36yy y−=−
Chapter 5 Exponents and Polynomials
24.
()
22
3736yyy−+−
()
() ()
22 2 2
43 2
37 3336
21 9 18
yy yyy
yy y
=−+ +−
=− + −
25.
()
53 2
28 10 1yy y−+
27.
()
()
2
324 35yyy−+−
()()
22
32 2
32
34 3524 35
12 9 15 8 6 10
12 21 10
yy y y y
yy yyy
yy y
=+−−+−
=+−−−+
=+−+
30.
()()
62xx++
2
2
26 62
2612
812
xx x x
xxx
xx
=⋅+⋅+⋅+⋅
=+++
=++
32.
()()
22
42 3xx−−
() ()
22 2 2
422
42
443223
412 2 6
4146
xx x x
xxx
xx
=⋅+ −−⋅−−
=− −+
=− +
36.
() ()()
222
2
3233
69
xxx
xx
+=+ +
=++
37.
( ) () ()()
22
2
34 3 23416
92416
yyy
yy
+= + +
=++
20
xx
=−−
43.
()()
2
2
34
4312
712
Ax x
xxx
xx
=+ +
=+++
=++
Chapter 5 Review Exercises
44.
()()
2
2
30 20
20 30 600
50 600
Ax x
xxx
xx
=+ +
=+ + +
=+ +
The area of the expanded garage is
()
22
50 600 yards .xx++
46.
2324
4 9 17 12xy xy x+−−
2
Term Coefficient Degree
44213
xy
+=
47.
()( )
222 2
78 894xxyy xxyy−++−−+
()
()
()
22 2 2
22
78 89 4
17 5
x x xy xy y y
xxyy
=−+−−++
=− − +
49.
()()
()()
23 46 2436
69
75 75
35
xy xy x y
xy
++
−=−−
=−
Chapter 5 Exponents and Polynomials
52.
()()
4391xy xy−−
() ()()()
22
22
49 4 139 31
36 4273
36 31 3
xy xy xy xy
xy xy xy
xy xy
=+−−−−
=−−+
=−+
56.
()
()
22
aba abb−++
()()
()( )
2222
32 22 23
322 2 23
33
aa ab b ba ab b
aababababb
aababababb
ab
=++−++
=+ + − − −
=+ − + − −
=−
59.
()
0
10 1−=
60.
()
0
10 1 1−=−=−
61.
0
400 400 1 400x=⋅=
65.
86 8 6 73
313
40 40 8
5
5
xy x y xy
xy x y
=⋅⋅=
66.
42 4 2
18 12 36 18 12 36
6666
xxxx x x
xxxx
−+
=−+
3
xy
32 2 2
2
27 9 18
333
936
xy xy xy
xy xy xy
xy x y
=−−
=−−
69.
2
2
27
22 3 14
2
x
xxx
x
+
−+−
−
70.
2
32
35
212 5 75
xx
xxxx
−+
+−++
32
2
2
6 7
xx
xx
+
−+
Chapter 5 Review Exercises
71.
2
32
52
72337
xx
xxx x
++
−−−−
32
32 2
7
2337 7
52
77
xx
xx x xx
xx
−
−−−
=+++
−−
22
y27 39
3
yy
y
−=++
−
73.
2
2 432
432
32
231
20146031
402
6 2 3
xx
xx xxxx
xxx
xxx
+−
++ + + +−
++
−+
74.
()
()
32
4321 1xx x x−−+÷+
1 4 3 2 1
475
−−−
−−
75.
()
()
42
321020 2xx x x−−−÷−
2 3021020
−− −
1 4 16 64 272
−−
()
()
4
32
16 4
272
41664 4
xx
xx x x
+÷+
=− + −+
+
77.
2
2
11
749
7
−
==
Chapter 5 Exponents and Polynomials
83.
66
2
88 2
30 30 6
6
5
5
yy
y
yy y
−
=⋅ = =
86.
()
()
4
334
412
10 10 10
12 10 2
3381
81 81
yyy
yyy
yy
−
==
==
89.
()
2
72
36
46
1xxx
xx
−−−
===
90.
()
()
()
4
312 12 8 20
48
2
yyyy
y
y
−−
−
−
== =
95.
4
0.00062 6.2 10
−
=×
1
−
15
4
510 10
5.0 10
−
=× ×
=×
100.
()
()
222
22 4
4 10 4 10 16 10
−
−−
×=× =×
Chapter 5 Test
1.
2
96 4xx+−
is a trinomial of degree 2.
2.
()
32
73511xxx+−−
()
32
62413xxx+−+−
Chapter 5 Test
4.
()
()
2
2
2
3(,)
3(3)363,6
2(2)312,1
xyx xy
y
y
=−
−=−−=−
−=−−=−
5.
()()
()
()
38 38 11
75 75 35xx x x
+
−=−⋅=−
6.
()
23
68 52xx x−−
7.
()
()
2
32 43xxx+−−
8.
()()
3729yy+−
9.
()()()
22
7575 7 5
xx x
+−=−
11.
( ) () ()()
22 2
2
53 5 2533
25 30 9
xxx
xx
−= − +
=−+
12.
2
456xy xy x+−
()
()
()
23 23 2 2
23 2
86 4210
2312
xy xy xy xy y y
xy xy y
=−+−+++
=++
22
12 13 35
aabb
=−−
15.
( ) () ()()()
22 2
22
23 2 223 3
xy x xy y
+= + +
12
5
5
5
xx
x
=−
5
x
43 2
15 10 25
xxx
Check by multiplication:
()
32
53 2 5xx x x−+
Chapter 5 Exponents and Polynomials
18.
2
32
23
212 3 4 4
xx
xxxx
−+
+−++
32
2
xx
+
Check by multiplication:
()
()
2
21 231xxx+−++
19.
()
()
43 2
31120 735 5xx xx x+− ++÷+
20.
2
2
11
10 100
10
−
==
21.
33
3
114 4 64
4
−
=⋅ = =
26.
() ()
22
424 28
88
2
55 5
25
5
xxx
xx
−−
−−− −
==
==
29.
6
7,600,000 7.6 10=×
31.
66
22
8.4 10 8.4 10
4
410 10
−−
×=×
×
10 16
xx
=+ +
Cumulative Review Exercises (Chapters 1-5)
1.
()()( )()()
75123 759
−−÷ −=−−÷
Cumulative Review
4.
()
232 4
262 4
xxx
xxx
++ =+
++ =+
3
5.
11
53102
xx
−= −
To clear fractions, multiply by the LCD = 30.
6. Let x=width of sign.
Then
32x−=
length of sign.
()
223228
xx
+−=
7.
78 6 5
78 6 6 56
27 5
xx
xx x x
x
−≤−−
−+ ≤−−+
−+≤−
Chapter 5 Exponents and Polynomials
8.
Principal Rate = Interest
12% Investment 0.12 0.12
14% Investment 0.14 0.14
xx
yy
×
Since the total investment is $6000, the first equation is 6000.xy+=
Solve for x.
0.12 0.14(6000 ) 772
0.12 840 0.14 772
0.02 840 772
y
xx
xx
x
+−=
+− =
−+=
9.
Number of Liters Percent Antifreeze = Amount of Antifreeze
70% Antifreeze Solution 0.70 0.70
30% Antifreeze Solution 0.30 0.30
xx
yy
×
Solve the first equation for y and substitute into the second equation.
20
20
xy
yx
+=
=−
Cumulative Review
10.
22
5
yx=− +
slope =
22
;
55
−
−=
y-intercept = 2
11. 24xy−=
x-intercept: 4
12.
()
21
21
42 6 6
235 5
yy
mxx
−−− −
== ==−
−−−
Because the slope is negative, the line is falling.
Chapter 5 Exponents and Polynomials
14.
32 10
43 15
xy
xy
+=
−=−
Multiply the first equation by 3 and the second
equation by 2:
15.
23 6
313
xy
yx
+=−
=−
Substitute the second equation in for y in the first
equation:
()
23 6
23313 6
xy
xx
+=−
+−=−
16. Let y = total charge.
Let x = # of bridge crossings.
without discount pass: 6yx=
with discount pass: 430yx=+
To find when they are the same, substitute the
18.
()()
53 53
93276379xxx xxx−+−− +−−
()( )
53 53
9327 6379
xxx xxx
=−+−+−−++
32 2
3 3
0
353 23
1
x
xxx xx
x
+
+++
=++
+
44
242 8
33 81
xx