Chapter 6
Exercises
an integer that is a factor of each integer.
monomials is the product of the greatest
common factor of the coefficients and, for
each variable, the variable to the lowest
monomials.
5
GCF
y yyyyy
y
= ⋅⋅⋅⋅
=
10.
4
33
55
GCF
aaaaa
a
=⋅⋅⋅⋅
=
12. 3
2
933
GCF 3 3
m mmm
mm m
=⋅⋅⋅⋅
=⋅ ⋅ =
2
32 22222
GCF 2 2 2 8
mn m n n
mn mn
= ⋅⋅⋅⋅⋅ ⋅⋅
= ⋅⋅⋅ ⋅ =
() ()
GCF 5 2
n
=+
18.
()()
()
44
GCF 4
yy y y
yy
−=⋅−
=−
() ()
()
()
()
2
65 1
y
=−
() ()
()
82
rt
=−
() ()
()
36
bb
=−
()
23
()
34.
() ()
32 23 22 22
35 3 5
pq pq pq p pq q
+= +
() ()
()
15 3
cd c d
=−
()
()
()
()
() ()
232
()
()
2
339
xx x
=−−
()
()
22
96
ccc
=++
Chapter 6 Factoring Polynomials
108
48.
() ()
()
()
33 2
12 9 15
34 3 5
mm m
=++
() ( ) ()
()
532
mn m n
=−+
52.
() () ()
24 3 3
322
18 24 30
xy xy xy
−+
()()()()
()()()( )
()()()()
()( )
11 2
nm
=− −
()()
()()()()
()()
()() ()()
()( )
22 3
xy
=− −
()()
()()
()()
52
ab
=− −
()()
()( )
265
bcac
=+ −
80.
()
()
1
1
11
SaNdd
SadN
dN
Sa
NN
Sa
=+ −
−= −
−
−=
−−
−
()
1
n
ar
S
S
+
(
)
() ()
()
() ()
()
2
74
mm
=−
22
1
12 12
12
1
bb bb
++
()( )
423
caba
=+ −
GCF 7
x
=
Section 6.2 Factoring Trinomials Whose Leading Coefficient Is 1
109
()
()
()
()
2
Hx y xy
xy xy
+=
++
b.
Reversing the order of the digits so
that
a is the digit in the thousands
place,
c is the digit in the tens place
()
()
()()
()
1000 100 10
9 111 10 10 111
abcd
dcb a
+++
=+−−
Since 9 is a factor of each term of
sion is divisible by 9.
(
)
b. 2
16 , 48,xxy−−
Coefficient Is 1
Exercises
written in descending order.
4. If each term in a trinomial has a common
()
()
()
()( )
Prime polynomial
()( )
()( )
()()
Chapter 6 Factoring Polynomials
110
()( )
()( )
712
xx
=− + −
()( )
()()
89
yy
=− −
()()
()
()()
42 5
yy
=− +
()
()( )
21 4
xx
=−−
()
2
523
zz
=−−
()( )
17
xx x
=+ −
()
67
qq q
=+ −
()()
()
()()
324
yy y
=−−
()
2
532
bb b
=++
()()
()
()( )
()()
2
49
by y y
=+−
()
()( )
()()
()()
()
Section 6.3 Factoring Trinomials Whose Leading Coefficient is Not 1
111
()()
()()
()
()( )
18
18
xx
⎜⎟
⎝⎠
=− − +
⎜⎟
⎝⎠
()( )
()
43
1
xx
x
−+
−
()
()
2
x
−
()
2
3
x
x
−
=−
Whose Leading
Exercises
()
28.
()()
49241 2nn n n−+= − −
()()
5232
nn
=+ +
()()
31 5
xx
=− −
()
()()
51 3
bb
=− − +
112
()
()
()
()
()()
32 1 7
xx x
=++
()
()()
2
521 3
nn n
=−−
()
()()
31 3
xy y y
=++
()
()()
22 3 4
sts t
=−+
()
(
)
(
)
42 3 2 3
abab
=− −
()
()
74.
()
2
24 6 18
xy xy xy
−−+
()
()
()( )
4521
xx
=+ −
()
()()
52331
ab a a
=−−
()
()( )
32 4 5
aab a b
=−+
()
92. a.
()
24rrrr
ππ
−=−
()
2
32 231
23
6
nn n
nnn
++
++
=
a. 7; 11
c.
2; 4−−
3. Answers may vary.
Trinomials, the Difference
or Difference of Cubes
Exercises
square, because the middle term is not twice
the product of a and 5b.
perfect squares.
22. Neither
()
()
()
()
()
()
()
()
()
()
2
12 1
y
=+
()
()
2
2
()()
()()
()()
114
()()
()()
()()
555
mm m
=+−
()
()()
3
31010
tt t
=+−
()()
()
()()
()()
()
()()
()
()()
22
()()()
(
)
11
aby y
=− + −
()()()
()
()
()
()
()
22
2
222
224
ttt
ttt
=− +⋅+
=− ++
()
()
22
aba abb
=− ++
()
()
()
()
22
333
339
xxx
xxx
=+ −⋅+
=+ −+
()
() ()
()
()( )
2
22 2 2
222
242
xxx
xxx
=− +⋅+
=− + +
()
()
()
2
32 24
xxx
=− ++
()
()
()
32
24 164
nn nn
=+−+
()
()
()
32
242
xx xx
=+−+
()()
()
()
()
()
()
()
2
339
mmm
=− ++
()
()()
45 2 5 2
tt
=+ −
Section 6.5 Solving Quadratic Equations by Factoring
115
()
()
2
16,000 1 2
16,000 1
rr
r
=++
=+
()
()
()
21
22
212 211
3
4
rrr rrr
π
=−+⋅+
2. a.
x
2
d.
33
xx
−−
g.
()
large outer square can also be represented by
the sum of the areas of the smaller interior
rectangles and squares. The area of the blue
square is
2,a the area of each green rectangle
22
2.aabb=+ +
Equations by Factoring
Exercises
equals to the square of the hypotenuse.
()
230
23
t
t
+=
=−
16.
()
25 4 0yy−=
20
y
=
or 540
y
−=
18.
()( )
33 1 0tt−−=
45
5
4
x
x
−=−
=
45
5
4
x
x
=−
=−
22.
()
12 0tt+=
116
()
()
30
0
t
t
=
=
or 12 0
21
1
2
t
t
t
+=
=−
=−
10
1
x
x
−=
=
or 20
2
x
x
+=
=−
290 0
()()
23 40
yy
−+=
230
23
3
y
y
−=
=
or 40
4
y
y
+=
=−
()( )
210
21
t
t
−=
=
or 230
23
t
t
−=
=
36.
2
025 10 1
yy
=++
5
()()
70
t
+=
or 70
t
−=
410
x
+=
()
()()
2
9210
91 10
tt
tt
++=
++=
10
1
t
t
+=
=−
()
()()
23 1 5 0
nn
−−=
310
31
n
n
−=
=
or 50
5
n
n
−=
=
46.
()()
310
rr
+=
20
2
r
r
−=
=
or 50
5
r
r
+=
=−
3
y
=−
4
y
=
50.
()()
2
318
tt
−=
30
t
+=
or 60
t
−=
52.
()()
317 10
kk
+=−
320
3
k
k
+=
=−
or 50
k
+=
117
54.
()
()()
12 33 9
34 1 3 0
xx
xx
+=
−+=
410
x
−=
or 30
x
+=
56.
()
2
36
mm
=
30
0
m
m
=
=
or 20
2
m
m
−=
=
()()
2
9160
34340
y
yy
−=
+−=
340
34
y
y
+=
=−
or 340
34
y
y
−=
=
60.
()
()()
2
12 48
220
x
xx
=
+−=
()()
64.
()
310
rr
+=
2
r
=
5
r
=−
(
)
()
()()
2
27120
23 40
nn
nn
++ =
++=
()()
()( )
2
5610
140
mm
mm
−−=−
−−=
10
1
m
m
−=
=
or 40
4
m
m
−=
=
()()
()()
2
2
31018
3280
470
tt
tt
tt
−− =
−− =
+−=
()()
()()
2
32516
31 50
xx x
xx
+−=
+−=
310
x
+=
or 50
x
−=
()
()( )
83 6
02 1 4
nnn
nn
+= −
=+−
()()
03 1
13
u
u
=+
−=
118
78.
()()
328
470
nn
nn
+=
−+=
80.
()
927
bb
=
2
4450
xx
−−=
73 0
m
−=
or 73 0
m
+=
2
650
nn
−=
90.
222
2
12 13
25 0
x
x
+=
−=
92.
()
()()
16 8 24 0
82 3 1 0
tt
tt
−++=
−−+=
2 or 1.5 sec.
()
()
1. a. Possible answer: 2560xx−+=
()
()()
20
2
x
x
+=
=−
or 50
5
x
x
−=
=
() ()
3. The zero-product property is true for more