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Mr. Simonds' MTH 65 Solutions: Mathematics Problem Sets, Assignments of Algebra

Portland Community CollegeAlgebra

Solutions to various mathematics problems presented in problem sets from mr. Simonds' mth 65 course. The problems cover topics such as algebra, number theory, and equations.

Typology: Assignments

Pre 2010

Uploaded on 08/16/2009

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koofers-user-7pb 🇺🇸

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Mr. Simonds’ MTH 65 – solutions by the numbers
Page 1 of 6
Problem Set 1
a.
()()
()()
22
12 32 4 8 32
48 4
84
xx xxx
xx x
xx
++=+++
=+++
=+ +
b.
()()
()()
22
38 72 2 36 72
236 2
36 2
yy yyy
yy y
yy
++=+++
=
++ +
=+ +
c.
()()
()()
22
18 72 6 12 72
612 6
12 6
xx xxx
xx x
xx
++=+++
=++ +
=+ +
d. 230 72xx
+
+ is prime
e.
()()
()
2
2
14 49 7 7
7
aa aa
a
++=+ +
=+
f.
(
)( )
291 90 90 1yy y y
+
+=+ +
g.
()( )
229 180 9 20tt tt++=+ +
h. 2424aa
+
+ is prime
Problem Set 2
a.
()()
()()
22
14 48 6 8 48
68 6
86
xx xxx
xx x
xx
−+=−−+
=−−−
=− −
b.
()()
()()
22
27 92 4 23 92
423 4
23 4
bb bbb
bb b
bb
−+=−−+
=
−− −
=− −
c. 229 92xx−+ is prime
d.
(
)( )
226 48 24 2yy y y
−
+=− −
e.
()()
216 60 10 6xx x x−+=− −
f.
(
)( )
230 81 27 3aa a a
−
+=− −
g. 227 27tt−+ is prime h.
(
)( )
()
2
2
30 225 15 15
15
mm m m
m
−+=− −
=−
Problem Set 3
a.
()()
()()
22
9 90 6 15 90
615 6
15 6
tt ttt
tt t
tt
+−=−+ −
=−+ −
=+ −
b.
()()
()()
22
524 3824
38 3
83
tt ttt
tt t
tt
+−=−+−
−+ −
=+ −
c.
()()
()()
22
15 100 5 20 100
520 5
20 5
zz zzz
zz z
zz
+−=−+ −
=−+ −
=+ −
d.
(
)( )
290 10 9yy y y
+
−=+ −
pf3
pf4
pf5

Partial preview of the text

Download Mr. Simonds' MTH 65 Solutions: Mathematics Problem Sets and more Assignments Algebra in PDF only on Docsity!

Problem Set 1 a.

x x x x x x x x x x

b.

y y y y y y y y y y

c.

x x x x x x x x x x

d. (^) x^2 + 30 x + 72 is prime

e. ( )( )

2 2

a a a a a

f. y^2^ + 91 y + 90 = ( y + 90 )( y + 1 )

g. t^2 + 29 t + 180 = ( t + 9 )( t + 20 ) h. a^2 + 4 a + 24 is prime

Problem Set 2 a.

x x x x x x x x x x

b.

b b b b b b b b b b

c. x^2^ − 29 x + 92 is prime d. y^2^ − 26 y + 48 = ( y − 24 )( y − 2 )

e. x^2^ − 16 x + 60 = ( x − 10 )( x − 6 ) f. a^2 − 30 a + 81 = ( a − 27 )( a − 3 )

g. t^2 − 27 t + 27 is prime h. ( )( )

2 2

m m m m m

Problem Set 3 a.

t t t t t t t t t t

b.

t t t t t t t t t t

c.

z z z z z z z z z z

d. y^2^ + y − 90 = ( y + 10 )( y − 9 )

e. m^2 + 20 m − 44 = ( m + 22 )( m − 2 ) f. p^2^ + 200 p − 100 is prime

g. x^2^ + 4 x − 24 is prime h. w^2 + 22 w − 240 = ( w − 8 )( w + 30 )

Problem Set 4 a.

x x x x x x x x x x

b.

t t t t t t t t t t

c.

p p p p p p p p p p

d. y^2^ − 2 y − 48 = ( y − 8 )( y + 6 )

e. x^2^ − 20 x − 48 is prime f. w^2 − 3 w − 180 = ( w − 15 )( w + 12 )

g. z^2 − 88 z − 180 = ( z − 90 )( z + 2 ) h. w^2 − 399 w − 400 = ( w − 400 )( w + 1 )

Problem Set 5 a.

x x x x x x x x x x

b.

w w w w w w w w w w

c.

y y y y y y y y y y

d.

y y y y y y y y y y

e.

b b b b b b b b b b

f.

t t t t t t t t t t

g.

2 2

2

x x x x x x x x x x x

h.

w w w w w w w w w w

g.

8 16 8 8 16 8 8 8 8 8

w w w w w w w w w w

h.

4 2 4 2 2 2 2 2 2 2

t t t t t t t t t t

i.

10 5 10 5 5 5 5 5 5 5 5 2

t t t t t t t t t t t

j.

m n m n m n m n m n m n m n m n m n m n

Problem Set 7

a. x^2^ − 81 = ( x − 9 )( x + 9 ) b. 4 w^2^ − 9 y^2 = ( 2 w − 3 y ) ( 2 w + 3 y )

c. 100 − 49 x^10^ = ( 10 − 7 x^5^ )( 10 + 7 x^5 ) d. y^42 − 25 x^2 = ( y^21 − 5 x )( y^21 + 5 x )

e. 49 x^2 − 1 = ( 7 x − 1 )( 7 x + 1 ) f. 121 − 9 w^4 = ( 11 − 9 w )( 11 + 9 w )

g. 36 x^18^ − 25 y^6^ = ( 6 x^9 − 5 y^3^ ) ( 6 x^9 + 5 y^3 )

Problem Set 8

a. ( ) ( )

3 6 2 2 2 2 2 2 2 4

t y t y t t y y t y t t y y

− = − ⎡^ + + ⎤

b. ( )

3 2 2 2

x x x x x x x

− = − ⎡⎣^ + + ⎤⎦

c. ( ) ( ) ( )( ) ( )

3 3 2 2 2 2

x y x y x x y y x y x x y y

+ = + ⎡⎣^ − + ⎤⎦

d. ( ) ( ) ( )

6 2 2 2 2 2 2 2 4

m m m m m m m

+ = + ⎡^ − + ⎤

e. ( ) ( ) ( )( )

3 2 2 2

t t t t t t t

− = − ⎡⎣^ + + ⎤⎦

f. ( ) ( ) ( )( )

9 3 3 2 3 2 3 6 3

x x x x x x x

+ = + ⎡^ + + ⎤

g. ( ) ( ) ( ) ( ) ( )

6 3 2 2 2 2 2 2 4 2 2

x y x y x x y y x y x x y y

+ = + ⎡^ − + ⎤

Problem Set 9 a. x^2^ + 81 is prime b. 4 w^2 + 9 y^2 is prime c. 100 + 49 x^10 is prime

d. y^4 + 25 x^2 is prime e. 49 x^2^ + 49 = 49 ( x^2 + 1 ) f. 121 + 9 w^4 is prime

Problem Set 10

a. ( )

x x x x x x

b. ( )

4 2 2 2 2

w w w w w w w

c. ( )

4 3 2 2 2 2 2 2 2

x x x x x x x x x x x x x x x x x

= ⎡⎣^ − + − ⎤⎦

d. ( )

7 5 3 3 4 2 3 4 2 2 3 2 2 2 3 2 2 3 2 2

t w t w t w t w t t t w t t t t w t t t t w t t t w t t

= ⎡⎣^ − − − ⎤⎦

= ⎡⎣^ − − ⎤⎦