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Official© Solutions Manual to Accompany Finite Mathematics and Calculus with Applications,Lial,9e
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  • July 21, 2024
  • 1282
  • 2023/2024
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Copyright © 2012 Pearson Education, Inc. Publishing as Addison-Wesley. 1 Chapter R ALGEBRA REFERENCE R.1 Polynomials Your Turn 1 22
22
23( 4 5) 4(3 5 7)
31 2 1 5 1 2 2 0 2 8
98 1 3xx xx
xx x x
xx-- - --
=-- - ++
=- + + Your Turn 2 2
22
32 2
32(3 2)(4 2 5)
(3 )(4 2 5) (2)(4 2 5)
12 6 15 8 4 10
12 2 19 10+- -
=- - + - -=- - + - -=+ - -yy y
yy y y y
yy y yyyy y R.1 Exercises 1. 22
22
2
2(2 6 11) ( 3 7 2)
26 1 1 37 2
(2 3) (7 6) (11 2)
9xx xx
xx xx
xx
xx-++ -+-
=- + -+ -=- +- +-=- + + 2. 22
22
22
22
2(4 3 8 ) ( 2 6 2 )
(4 3 8 ) (2 6 2 )
43 8 26 2
(4 2 ) (3 6 ) ( 8 2 )
63 1 0yy yy
yy y y
yy yy
yy y y
yy--+ - --
=- - + +- + +=- - + - + +=- - +- + + +
=- + + 3. 22
2
2
22
26(2 4 3) 4( 7 3)
(1 2 2 4 1 8 )
( 4 28 12)
(1 2 4 )
( 24 28 ) (18 12)
16 4 6qq qq
qq
qq
qq
qq
qq-+ - + - + -
=- - +
+- + -
=- -
+- + + -
=- + + 4. 22
22
22
22(3 4 2) 3 ( 4 5)
(6 8 4) (3 12 15)
(6 3 ) (8 12 ) (4 15)94 1 9++- - +-
=+ + +- +=++ -+ +=- +rr rr
rr r rrr rr
rr 5. 22
22
2(0.613 4.215 0.892) 0.47(2 3 5)
0.613 4.215 0.892 0.94
1.41 2.35
0.327 2.805 1.458-+- - +
=- + -
+-
=- - -xx x x
xx x
x
xx 6. 22
22
22
20.5(5 3.2 6) (1.7 2 1.5)
(2.5 1.6 3) ( 1.7 2 1.5)
(2.5 1.7 ) (1.6 2 ) ( 3 1.5)0.8 3.6 1.5+- - - -
=+ - + - + +=-+ + + - +=+ -rr r r
rr r rrr r r
rr 7. 2
2
329( 2 3 1 )
9( 2 ) 9( 3) 9(1 )18 27 9mm m
mm mm m
mm m-+ -
=- - - -=- - + 8. 34 26 ( 2 5 6) 12 30 36x x x xxx-++ = - + + 9. 22
22(3 2 )(3 5 )
(3 )(3 ) (3 )(5 ) ( 2 )(3 ) ( 2 )(5 )
91 56 1 099 1 0-+
=++ - + -=+--=+-ty ty
tt t y yt y y
tt y t y ytt yy 10. 22
22(9 )(2 )
(9 )(2 ) (9 )( ) ( )(2 ) ( )( )
18 9 2
18 7+-
=+ - + + -=- + -=- -kq kq
kk k q qk qq
kk q k q qkk q q 11. 2
2(2 3 )(2 3 )
(2)(2) (2)(3 ) ( 3 )(2) ( 3 )(3 )
4 66949-+
=+ + - + -=+ - -=-xx
xx x x
xxx
x 12. 2
2(6 5)(6 5)
( 6 ) 6 )( 6 ) ( 5 )( 5 ) ( 6 )( 5 ) ( 5 )
36 30 30 2536 25+-
=+ - + + -= -+-=-mm
mm m m
mm mm 2 Chapter R ALGEBRA REFERENCE Copyright © 2012 Pearson Education, Inc. Publishing as Addison-Wesley. 13. 21 31
58 52
23 21 1 355 52 8 5
11
82æö æö÷÷ çç++÷÷ çç ÷÷÷÷ ççèø èø
æö æö æö æö æö æö÷÷ ÷÷ ÷÷çç çç çç=++÷÷ ÷÷ ÷÷çç çç çç÷÷ ÷÷ ÷÷÷÷ ÷÷ ÷÷çç çç ççèø èø èø èø èø èø
æö æö÷÷çç+÷÷çç÷÷÷÷ççèø èøyz yz
yy yz zy
z z 22
22
226131
25 5 40 16
68 3 1
25 40 40 16
61 1 1
25 40 16yy zy zz
yy z z
yy z z=+ ++
æö÷ ç =+ + + ÷ ç ÷÷ çèø
=++ 14. 32 51
43 43
35 31 25
44 43 34
21
33æö æö÷÷ çç-+÷÷ çç ÷÷÷÷ ççèø èø
æö æöæö æöæ ö æö÷÷ ÷÷ ÷÷çç çç ç ç=++ -÷÷ ÷÷ ÷÷çç çç ç ç÷÷ ÷÷ ÷÷÷÷ ÷÷ ÷÷çç çç ç çèø èøèø èøè ø èø
æö æ ö÷÷çç+-÷÷çç÷÷÷÷ççèø è ørs rs
rr rs sr
ss 22
221 5 152
16 4 6 9
15 7 2
16 12 9rr s r s s
rr s s=+ - -=- - 15. 2
2
22
322
3(3 1)(9 3 1)
(3 1)(9 ) (3 1)(3 ) (3 1)(1)
3 ( 9)1 ( 9) 3 ( 3 )
1(3 ) 3 (1) 1(1)
27 9 9 3 3 1
27 1-+ +
=- +- +-
=- +
-+-
=- + - + -
=-pp p
pp pp p
pp p pp
pp
pppp pp 16. 2
2
2
32 2
32(3 2)(5 4)
(3 )(5 ) (3 )( ) (3 )( 4)
(2)(5 ) (2)( ) (2)( 4)
15 3 12 10 2 8
15 13 10 8pp p
pp p p p
pp
pp pppppp++ -
=+ + -
++ + -
=+ - ++ -=+- - 17. 2
22
32 2
3(2 1)(4 2 1)
2 (4 2 1) 1(4 2 1)
84 2 42 1
81mm m
mm m m m
mmm mmm+- +
=- + + - +=-+ +- +=+ 18. 32
32
32
43 2 32
43 2(2 ) ( 1 2 3 1 )
(12 ) ( 3 ) ( ) (1)
2 ( 1 2 )2 ( 3 )2 ( )2 ( 1 )
12 3 24 6
22
12 21 5 3 2+- + +
=+ - + +
++ - + +
=- + + +-
++
=+- + +kk k k
kk k k k k k
kk k
kk k k kk
k
kk k k 19. 22
2
22 2() ( 3 2 )
( 3) ( 2) ( ) ( 3) ( 2)
() ( 3 ) ( 2 ) ()
32 32 3
2
32 2 3++ - -
=+ - + - ++ -
+-+ +- +-
=-- +-- +
--
=+ +---xyz x y z
xx x y x z yx y y
yz z x z y zz
x x y x zx yyy zx z
yz z
x xy xz y yz z 20. 2
22
22 2(23 ) ( 22 )
( 2) ( 2) () 2( 2) 2( 2)
2 ( )3 ( 2 )3 ( 2 )3 ( )
22 42 6 6
32
22 5 48 3+- -+
=+ - + + + -
+- - - -
=-+ ++ - +
-+- +
=+ - -+ -rs t rs t
rr r s r t sr s s
stt rt st t
rr s r t r s s t r t s t
tr t s t t
rr s r t ss t t 21. 2
2
2
32232(1 ) (2 ) (3 )
[ ( 2) 1( 2)]( 3)
[2 2 ] ( 3 )[3 2 ] ( 3 )
(3 ) 3 (3 ) 2 (3 )
339 2 661 1 6+++
=+ + + +=+ + + +=+ + +
=+ ++ + +
= +++ + +=+ + +xx x
xx x xxx x xxx x
xx x x xxxxx xxx x 22. 2
2
2
32 232(1 ) ( 2 ) (3 )
[ ( 2) ( 1)( 2)]( 3)
(2 2 ) ( 3 )
(2 ) ( 3 )
(3 )(3 ) ( 2 ) (3 )
33 2 6
25 6-+-
=+ + - + -=+ - --=+ --
=- + - + - -
=- +--+=- -+xx x
xx x x
xx x xxx x
xx x x xxx xx xxxx 23. 2
2
2(2 )(2 ) (2 )
(2 ) 2 (2 )
224
44xx x
xx xxx xxx+= + +
=+ ++=+++=++ Section R.2 3 Copyright © 2012 Pearson Education, Inc. Publishing as Addison-Wesley. 24. 2
22
22(2 4 ) (2 4 )(2 4 )
2( 2 4) 4( 2 4)
4881 641 61 6ab ab ab
aa b ba baa b a bbaa b b-= - -
=- --=--+=- + 25. 3
22
22(2 )
[( 2 )( 2 )]( 2 )
(224 ) ( 2 )
(44 ) ( 2 )-
=- - -=--+ -=-+ -xy
xy xy xy
xx y x y y x yxx y y x y 22
22
32 22 23
32 23(44 )
(44 ) ( 2 )
44 28 8
61 28=-+
+-+ -
=- + - + -
=- + -xx y y x
xx y y y
xx y x yx y x yyxx yx yy 26. 32
22
32 2 2
23
32 2 3(3 ) (3 )(3 )
(3 )(9 6 )
27 18 3 9
6
27 27 9xy xy xy
xy x x yy
xx y x y x y
xy y
xx y x y y+=+ +
=+ ++=+ ++
++
=+ ++ R.2 Factoring Your Turn 1 Factor 43 244 1 8 .z zz++ 43 2
22 2 2
2244 1 8
( 2 )2 ( 2 )2 ( 2 )9
(2 )(2 2 9)zz z
zz zzzzz z++
=⋅ +⋅ +⋅
=+ + Your Turn 2 Factor 22654 .aa b b+- 22654 ( 2) ( 3 4 )aa b b a b a b+-=- + R.2 Exercises 1. 32 2 2
271 4 7 7 2
7( 2 )aa a a a
aa+= ⋅ + ⋅
=+ 2. 32 2
232 49 3 3 8 3 3
3( 8 3 )yy y y y y y y
yy y+ +=⋅+⋅+⋅
=+ + 3. 42 3 22
22 2 2
2213 39 26
13 13 3 13 2
13 ( 3 2 )pq pq pq
pqp q p q p p q q
pq pq
p q-+
=⋅ -⋅ +⋅
=- + 4. 432 2
22 2 2 2
22 260 120 50
10 6 10 12 10 5
10 (6 12 5 )-+
=⋅ -⋅+⋅
=- +mm n m n
mm m m n mn
mm m n n 5. 251 4 (7 ) ( 2 ) mm m m--=- + since ( 7)(2) 14-= - and 7 2 5.-+ = - 6. 245 (5 ) (1 ) xx xx+- =+ - since 5( 1) 5-= - and 1 5 4.-+ = 7. 292 0 (4 ) (5 ) zz z z++=+ + since 4 5 20⋅= and 4 5 9.+= 8. 287 (7 ) ( 1 ) bb b b-+ =- - since (7 ) (1 ) 7--= and 7 ( 1) 8.-+- = - 9. 2265() ( 5 ) aa b ba b a b-+= -- since 2() ( 5 ) 5bb b-- = and ( 5 ) 6 . bb b-+- = - 10. 2223 5 ( 5 ) ( 7 ) s st t s t s t+- = - + since 2(5 ) ( 7 ) 3 5tt t-= - and 7( 5 ) 2 .tt t+- = 11. 2242 1 ( 3 ) ( 7 ) yy z zy z y z-- = + - since 2(3 )( 7 ) 21z zz-= - and 3 ( 7 ) 4 . z zz+- = - 12. 234 7xx+- The possible factors of 3 x2 are 3 x and x and the possible factors of –7 are –7 and 1, or 7 and –1. Try various combinations until one works. 234 7 ( 3 7 ) ( 1 )xx x x+- = + - 13. 231 0 7aa++ The possible factors of 3 a2 are 3 a and a and the possible factors of 7 are 7 and 1. Try various combinations until one works. 231 0 7 ( 1 ) ( 3 7 )aa aa++ = + + 14. 215 2 (5 2)(3 1)yy y y+-= + - 15. 2221 13 2 (7 2 )(3 )++ = + +mm n n m n m n 16. 226 48 120 6( 8 20)
6( 10)( 2)aa a a
aa--= - -
=- + 17. 32 231 2 9 3 ( 4 3 )
3( 1 ) ( 3 )mm m m m m
mm m++ = + +
=+ + 18. 2241 0 6 2 ( 25 3 )
2(2 3)( 1)aa a a
aa++ = + +
=+ + 4 Chapter R ALGEBRA REFERENCE Copyright © 2012 Pearson Education, Inc. Publishing as Addison-Wesley. 19. 432 2
22 2
224 10 4
2( 1 2 5 2)
2( 4 ) ( 3 2 )aa b a b
aa a bb
aab a b+-
=+ -
=- + 20. 43 2 2
22 2
224 36 60
12 (2 3 5 )
12 ( )(2 5 )xx y x y
xx x y y
xx y x y+-
=+ -
=- + 21. 22 264 8
(8 ) (8 )xx
xx-=-
=+ - 22. 22 292 5 ( 3 ) ( 5 )
(3 5)(3 5)mm
mm-= -
=+ - 23. 22
2210 160 10( 16)
10( 4 )
10( 4)( 4)xx
x
xx-= -
=-
=+- 24. 296 4x+ is the sum of two perfect squares. It cannot be factored. It is prime. 25. 22 2 2 2
214 49 2 7 7
(7 )z zy y z zy y
zy++ = + ⋅ +
=+ 26. 22 2 2
210 25 2 5 (5 )
(5 )s st t s st t
st-+ = - ⋅ +
=- 27. 22 2
292 4 1 6 ( 3 ) 2 3 4 4
(3 4)pp p p
p-+ = - ⋅ ⋅ +
=- 28. 33 3
22
2216 6
( 6)[( ) ( )(6) (6) ]
(6 ) ( 63 6 )aa
aa a
aa a-= -
=- + +
=- ++ 29. 33 3 3
2227 64 (3 ) (4 )
(3 4 )(9 12 16 )rsr s
rs r r s s-=-
=- + + 30. 33
33
23 375 3( 125)
3( 5 )
3( 5)( 5 25)mm
m
mm m+= +
=+
=+ - + 31. 44 2 2 2 2
22 22
22() ()
() ()() ( ) ( )xy x y
xy xy
xy x y x y-= -
=+ -
=+ + - 32. 44 2 22 2
22 22
222 2
2216 81 (4 ) (9 )
(4 9 )(4 9 )
(4 9 )[(2 ) (3 ) ](4 9 )(2 3 )(2 3 )ab a b
ab abab a bab a b a b-= -
=+ -=+ -=+ + - R.3 Rational Expressions Your Turn 1 Write in lowest terms 2
256.
27 3zz
zz++
++ 2
256 (3 ) (2 )
(3 ) ( 21 ) 27 3
2
21zz z z
zz zz
z
z++ + +=++ ++
+=+ Your Turn 2 Perform each of the following operations. (a) 22
2256 2 1
25 3 2 3
2)( 3) (2 1)( 1)
(2 1)( 3) ( 3)( 1)
(2 ) (3 )zz z z
zz z z
zz z z
zz zz
zz++ - -⋅
-- +-
(+ + + -=⋅+- +-
++=(2 1)z+ (1 )z-
(2 1)z+(3 ) (3 )zz-+ (1 )z-
2
3z
z+=- (b) 2235
32 4
35
( 2)( 1) ( 2)( 2)
3( 2 )
(2 ) (1 ) (2 )
5( 1 )
(2 ) (2 ) (1 )-+
++ -
-=+++ -+
--=⋅++ -
++⋅-+ +aa
aa a
aa
aa aa
aa
aa a
aa
aa a 22
2
2(5 6 ) ( 55 )
(2 ) (2 ) (1 )
66
(2 ) (2 ) (1 )
6( 1)
(2 ) (2 ) (1 )-++ +=-++
+=-++
+=-++aa aa
aaa
a
aaa
a
aaa R.3 Exercises 1. 255
35 5 7 7vv v v
vv⋅⋅==⋅⋅ 2. 3
225 5 5 5
25 2 10p ppp p
pp p⋅⋅⋅⋅==⋅⋅⋅

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