Chapter 6 Factoring Polynomials
106.
2
4yx x=−
To match this equation with its graph, find the
intercepts.
To find the y−intercept, let 0x=and solve for .y
107.
2
2
34
340
yx x
xx
=+−
+−=
Graph
2
34yx x=+− and use the graph to find the
x-intercepts.
108.
2
2
6
60
yx x
xx
=+−
+−=
The x–intercepts for the graph are −3 and 2. This
66 0
00, true
−=
=
109.
()()
236
yx x
=− +−
Chapter 6 Review Exercises
110.
2
2
21
210
yx x
xx
=−+
−+=
111. Answers will vary depending on the exercises
chosen.
112. Answers will vary depending on the exercises
chosen.
113. 21
yx=− + is a line with slope 22
−
−=
114.
()
()
2
42
47 3
7
2
23 6
6
88 2
4
4
4
24
xxx
x
xx
x
−−
−−
=⋅ =
=⋅ = =
115. 52866
5628666
xx
xx xx
+=−
++=−+
117. When x is replaced with 4, the denominator is 0.
Division by zero is undefined.
7 287(4)2828280x−= −=−=
Chapter 6 Review Exercises
1.
()
30 45 15 2 3xx−= −
2.
()
32 2
12 16 400 4 3 4 100xx xxxx+− = +−
6.
()
()
()()
()
()
32 32
2
2
326 3 26
32 3
32
xxx xx x
xx x
xx
+++=+ ++
=+++
=+ +
7.
()()
()()
44 44
14 1
xy y x xy y x
yx x
++ += + + +
=+++
Chapter 6 Factoring Polynomials
11.
()()
2
20 5 4xx x x−− = − +
16.
()
()()
22
36243 28
34 2
xx xx
xx
+−= +−
=+ −
19. Factor
2
5176yy−+ by trial and error or by
grouping. To factor by trial and error, start with the
First terms, which must be 5y and y. Because the
middle term is negative, the factors of 6 must both
be negative. Try various combinations until the
correct middle term is obtained.
()()
2
51 65 316
yy y y
−−=−+
21. Factor
2
5114yy++ by trial and error. The first
so
5114yy++ is prime.
22. First factor out the GCF, –2. Then factor the
resulting trinomial by trial and error or by grouping.
22
8862(443)
xx xx
−−+=− +−
26.
()()
22
568 54 2xxyy xyxy−− =+ −
27.
() ( )( )
2
22
412 12121xx xx−= − = + −
28.
()
()()
2
22
81 100 9 10
910 910
yy
yy
−=−
=+ −
Chapter 6 Review Exercises
33.
()
()()
32
9913131xxxx xx x−= − = + −
36.
()
()
222
2
16 64 2 8 8
8
xx x x
x
−+=−⋅+
=−
37.
() ( )
()
2
22
2
948643 2388
38
yy y y
y
++= + ⋅+
=+
40.
22
36 60 25xxyy++
() ( )()
()
22
2
62655
65
xxyy
xy
=+⋅+
=+
41.
22
25 40 16xxyy−+
() ( )( )
22
52544
xxyy
=−⋅+
44.
33
54 16xy−
33
45.
()
()
()()
()
()
33
33
22
2
27 8 27 8
32
323 322
329 64
xy y y x
yx
yx x x
yx x x
+= +
=+
=+ −⋅+
=+ −+
Area of each small corner square =
b
Area of four corner squares =
2
4b
Area of shaded region
()()
22
4
22
ab
abab
=−
=+ −
48. Area on the left:
Area of large square =
2
A
Area of each rectangle: 1AA⋅=
Area of two rectangles = 2A
Chapter 6 Factoring Polynomials
53.
73 34
20 36 4 (5 9)xx xx−+ =− −
55.
2
16y+is prime because it is the sum of two
squares with no common factor other than 1.
32 2
58.
()
()
()
()
5223
23 3
22
324 3 8
32
3224
xxxx
xx
xx x x
−= −
=−
=−++
61.
2
983xx+− is prime because there are no two
integers whose product is 27ac =− and whose sum
is 8.
65.
()
2
422
11
xx
−= −
()
()
2
22 24
yyy
=− ++
67.
333
64 4
xx
+=+
69.
()
()()
2
312 3 4
322
xxxx
xx x
−= −
=+−
70.
()()
2
90 10 9xx x x−− = − +
()
()
5525
xx x x
=+ −+
73.
()
32 2
32 32 6 2 16 16 3
yyyyyy
++= ++
Chapter 6 Review Exercises
77.
22
92416xxyy++
() ( )( )
()
22
2
32344
34
xxyy
xy
=+⋅+
=+
80.
22
xxyy++is prime.
Note that to be a perfect square trinomial, the
middle term would have to be 2xy.
81.
()
()()
42 24 22 2 2
22
312 3 4
322
xy xy xy x y
xy x y x y
−= −
=+−
{
}
84.
()()
2
5140
720
xx
xx
+−=
+−=
7 0 or 2 0
7 2
xx
xx
+= −=
=− =
{
}
86.
()()
2
2
2158
21580
21 80
xx
xx
xx
+=
+−=
−+=
87.
()
()()
2
2
432
432
4320
480
xx
xx
xx
xx
−=
−=
−−=
+−=
4 0 or 8 0
4 8
xx
xx
+= −=
=− =
The solution set is
{
}
4,8 .−
()
70
70
7
x
x
x
−=
−=
=
The solution set is
{
}
7.
Chapter 6 Factoring Polynomials
91.
2
321300
xx
++=
92.
()()
2
2
3227
32270
31 7 0
xx
xx
xx
=−
−+=
−−=
93.
2
16 16 32htt=− + +
Substitute 0 for h and solve for t.
2
0161632
tt
=− + +
94. Let x = the width of the sign.
Then x + 3 = the length of the sign.
Use the formula for the area of a rectangle.
()()
340
lw A
xx
⋅=
+=
95. Area of garden =
()
388xx−=
11 8
xx
==−
Because a length cannot be negative, reject x = −8.
Each side of the square lot is 11 meters, that is, the
dimensions of the square lot are 11 meters by 11
meters.
()
2
7
x
=−
3.
()
43222
2
15 35 10 5 3 7 2
531 2
yyyyyy
yy y
−+= −+
=−−
6.
()
()()
32 2
67 67
71
xxxxxx
xx x
+−= +−
=+ −
7.
22
14 64 30 2 7 32 15
xx xx
+−= +−
Chapter 6 Test
11.
24x+
is prime.
14.
2
16 48 36xx++
()
() ( )
()
2
22
2
44 12 9
42 223 3
42 3
xx
xx
x
=++
=+⋅+
=+
18.
32
2510xxx+−−
()
()
()()
()
()
32
2
2
2510
25 2
25
xx x
xx x
xx
=+ +−−
=+−+
=+ −
19.
32 2
12 12 45 3 (4 4 15)
3(2 3)(2 5)
yy yyyy
yy y
−+ +=− −−
=− + −
20.
333
125 5
yy
−=−
22.
22240
xx
+−=
23.
()()
2
352
3520
31 2 0
xx
xx
xx
−=
−−=
+−=
3 1 0 or 2 0
3 1 2
1
xx
xx
x
+= − =
=− =
=−
{
}
25.
()
2
2
621
6210
32 7 0
xx
xx
xx
=
−=
−=
3 0 or 2 7 0
0 2 7
7
2
xx
xx
x
=−=
==
=
The solution set is
7
0, .
2
Chapter 6 Factoring Polynomials
27.
()()
2
2
54 12
542
560
xx
xx
xx
+−=
−−=
−−=
29.
2
16 80 96htt=− + +
Substitute 0 for h and solve for t.
2
2
0168096
016(56)
016(6)(1)
tt
tt
tt
=− + +
=− − −
=− − +
6 0 or 1 0
6 1
tt
tt
−= +=
==−
Cumulative Review Exercises (Chapters 1-6)
1.
() ()
[]
()
65 23 8 3 65 2 5 3
65 10 3
68 48
+−−= +−−
=−−
=−=−
2.
()()
42243
48283
4858
xxx
xxx
xx
−= −+
−= −+
−= −
4.
()
55 25 1xx−> −+
55 102 1
55 112
55 2 112 2
53 11
53 5115
36
36
xx
xx
xx xx
x
x
x
x
−>−+
−>−
−+ >−+
−>
−−>−
−>
−<
6. Let x = the cost of the dinner before tax.
0.06 159
1.06 159
1.06 159
1.06 1.06
150
xx
x
x
x
+=
=
=
≈
The cost of the dinner before tax was $150.
Cumulative Review
7.
33
5
yx=− +
slope =
33
;
55
−
−=
y-intercept = 3
Plot (0,3). From this point, move 3 units down
8. First, find slope
()
14
55.
32 1
m−−
===
−
Use the point (2, −4) in the point-slope equation.
5 14
yx
=−
9.
224
3 4 4
235
xyz
xy z
xy z
−+=
−+ =
+− =
Multiply the third equation by 2 and add to the first
equation.
224
xyz
−+=
()
59
519
510
2
xz
x
x
x
+=
+− =
=
=
Back-substitute 2 for x and
1−
for z in one of the
10.
5213
27
xy
yx
+=
=−
The substitution method is a good choice for
91413
927
3
x
x
x
−=
=
=
Back-substitute into the second given equation.
()
27
23 7 1
yx
y
=−
=−=−
Chapter 6 Factoring Polynomials
Instead of back-substituting
2
13
−
and working with
fractions, go back to the original system and
12.
49 4895
58 5885
32 45 13
40 40 40
−=⋅−⋅
=−=−
14.
()()
35 29xyxy−+
22
22
6271045
61745
xxyxyy
xxyy
=+ − −
=+ −
16.
3
0.0071 7.1 10
−
=×
To write 0.0071 in scientific notation, move the
decimal point 3 places to the right. Because the
18.
()
()()
()
()()
54
22
2
16 16
44
422
yyyy
yy y
yy y y
−= −
=+ −
= ++−
Then x + 2 = the length of the rectangle.
Use the formula for the area of a rectangle.
()()
2
224
224
lw A
xx
xx
⋅=
+=
+=