Name
_
Date
_
Dividing Monomials
18x6 y
-3x3
18
x6 - 3
YS =--=J • -1-· r
1.
m
_
18x y =
24xy
11.
­
56s t
4s 2 t
=
12.
48a 3 be 5
12a5 b 3 e 2
2x 2 y2 ­
3.
4ab
2a 2 b 2
6.
7.
8.
2
10.
2.
5.
=7
9. 5x
=
5
=
X3 y 2
4.
-6x3
4
10
m-5
1
3
27JJ
'18Jv"
13e9 d 10
2 3
=
25x2y _
-26e9d =
13.
3ft
-3R=
14.
-52x3V-z _
15.
-17e d
-51ed 3
13XV ­
8xy2
16x3 y 5 =
Published by Instructional Fair, Copyright protected,
-15XV ­
8m 2 n 2
12m 2 n 3
5
16.
­
­
4
=
2
24x y3 Z4
-44X4 y3z2 =
Page 54
0-7424-1788-3 Algebra
Answer Key
From Factors to Equations
EKompkt: II") and
f
x + I = 0 and 3x - 2 = 0
2. Use the expressions as foctors of on equaflon.
3. Expand the factored form.
(X+ 1) (3x- 2)
4. Simplify.
3x2+x-2=O
~
II
ore the solutions, what was the equatIon?
Use the soIulk>ns 10 wrlle sImple equations equal to zero.
1.
g
Dividing Monomials
SInce foc1ored founs of equaflons con be used to delermlne ",8 solutions, solutio
be used to d91ermlne the equation. Just IeY91$6 the ~utIon process.
=a
'3
m lO
3x2 - 2x+ 3x- 2 = 0
(;5=
18
",,-J
1
'61<'
=~·-1-·Y==7
I
5><'
9. 5 =
m5
I'
Use the gl....en solullons 10 write 9qu01lons. Shode the regions below containing the equations.
6.
I
x .. -;. "8
2.
2. xc."7,"2
x+7=0 x+2=0
~+7)(X+2j=O
+2x+7x+14=0
I
2:
3
4:
~=
3,
40b J
20 2 b 2 =
4.
"I&Tv" =
X
10.
2
2b
0
XZ+9X+14=O
II.
3
27J-J
12.
~
3x
4
lax 2 y
24xy =
56s't'
14r
4:S'If =
4c3
480 3 bc5
120 5 b 3 c 2 =
(lfl
I
4.
2'
x=
3
2x
1.
i
5. x .. -
3
I
=0 x -
3
=0
5.
~tH;i=lJ
4'
~.
2
cf
"26c"d '"'
-2
3N
6. "3H=
~IN~&~;?:QQ
~:
13c9 d 1O
r+2x+24::10
r-9x-14=O
I
-4x2 z
~=
I
8.
l6x'Y" =
A CUBIC
r
+6(+5
0 2 +20
((
0+2
a
2. - - 7 - =
4 y2 + 6y
3. -2-y-=
(
.17e'd'
c4d
9.
12v'-27v' + 18u'?
3lN'
2x+5
10.
2y+ 3
2x' - IOxy
11. --2-x-
x- Y
12.
llX'
(56"
II~
_~
X+
1
13, --3-z--=
6, 12x' - 9'" + 6><'
3x
.;-
6Ql +420+ 72
60'
4x- 3; + 2;
64><'-64-'"
15, ~ =
mn +.l. - 1.
n
8,
203 + 0 2 -30
60 3 + 50 2 _ 60
0-1
30-2
x+4
x-4
9.
x 2 -9
x 2 +x-6
x-3
x-2
-4
0+4
10.
~=
t 2 + 4t- 5
t 2 + 9t+ 20 =
t- 1
t+ 4
11.
:<2 + 5:<
x 2 -25
5,
z'l-4z-5
Z2+ 4Z -45=
z+ 1
z+ 9
12,
0 2 _ 110 + 30
a 2 -90+18
6.
6b J - 24b 2
b 2 + b-20 =
7.
-x' + 8x- 12
~
c;et;i =
2.
~=
3.
12 ­ 40
0 2 +0-12
4.
9v
x- 5y
2
2
=
Y - XV + Y
2z-1+~
12
1 7
Ci+c;+C1
x-1
m
6Odb 2 -150 2b
=
"150 2b
x 2 +8x+16
2
14,
m 2n 2 +m_n
8
o+b
8a-8b
1.
4---+6
u
u
3x y' - 6x'r' + 6xy' - ;
3xy
-
6z 2 -3z+9
'5
-
6l
24>~Z:=
z
14k m) - 4k 2 m 'l + 12km 3
=
2km 2
7~m - 2k+ 6m
25u2 -15u-5
4502 b 4
3
'44
5x + 30x- 3S _ .6'(x + 7l-f!<:"1l
- ;8"(X+ 1) U<--t'i ­
5 - 5x 2
II
J
x'y-xy' ,
xy
mn
16.
W
"Sled J =
2
(
-5J + 3u+ 1
8.
2
3n
9
14x + 35
7.
6m 2 n 2
12m 2n J =
Simplifying Fractions
={+~+~-(+6+~
(
15.
1
8xy'
Dividing a Polynomial by a Monomial
5.
14.
7,
+ x-h. 0
The femolnlng letters spelllhe name of the type of equollon In problem 9:
4.
-1
5x
3y
~=
'I
i~:ti±gW-Q
Three solutions mean three faelors.
1.
13 '
16.
18m 3n 4
-383 + 40b+ 1
Published by Instructional Fair. Copyright protected.
-
12m 2n 3 + 24n 2
=
6m 2n
3mnJ
6~
b+5
6-x
13.
14.
=
3:<2+2x-1
3x- 1
x+ 2
X
=
x-5
2y' ­ 12y' + 2y
y" -6y+
a+b
1
0 2 + 2ab"+'t1 =
0-5
0-3
2y
1
o+b
-2n2+~
Page 115
0-7424- 1788-3 Algebra
Name
Incredible Irony
Believe it or not, the people of Washington, D.C., did not always have the right to
vote for the position of President of the United States. How many Presidents had
the United States had before these people were allowed to vote?
To find out, simplify each term. Match your answers to those given. Write the letter
corresponding to the solution above each problem number at the bottom of the page to spell
out the answer.
1.
x 2y
xy
1
2.x
2.
-Q2y
18xy
3.
10x2y
10x2y
T. x
4.
13xy
26x2y
Y.~
xy
5.
(9y)3
9y
x.
6.
-18xy2
6x2y 3
7.
-1Q2y
9xy4
8.
(-3.xy)( 6x2y4)
9.
(3x 2)3(2xy)
6xy
2
9x6
( ... '···111.
T. 81 y 2
9x3y 2
1
a
R.
I. 1
......
3
FS122010 Algebra Made Simple • © Carson-Dellosa
4
5
6
-
7
8
9
I Dividing exponents
~
8. V = (4, -2), opens down
3.
4.
Page 54
9. V = (5, 1), opens up
1.
Has many solutions
2.
Has no solution
four
3.
Has no solution
Page 43
T. x < 10
I. x> -22
A. x ~ 11
L. x s 25
4.
Has many solutions
10. V
=(3, -5), opens down
5. Has no solution
A. x ~ 19
O. x> -2
E. x < -14
E. x <-8
N. x> 47
E. x~6
N. x s-2
H. x ~ 2
H. x> -3
C. x> -6
5.
6.
y
III
6.
Has many solutions
7.
Has no solution
8.
Has no solution
9.
Has many solutions
Bugs Bunny
Page 55
An ace in the hole!
7.
Page 44
1. xs-2orx>8
2. 1 s x s 7
8.
y
1.
Quadrants I, II, III, IV
2.
Quadrant II
3.
Quadrants I, II, III
4.
Quadrants I, III, IV
3. -10<x< 10
5.
Quadrants I, II
4. x < -7 or x ~ 8
5. -3 s x < 5
6. x < 2 or x> 5
7. x ~ 9 or x s 7
8. x < -3 or x ~ 5
6.
Quadrant I
7.
Quadrants I, IV
8.
Quadrants II, III
10.
9.
Thriller (Michael Jackson)
Page 58
1. 30
2. 32x5
3. x 15
6
7
4. 30x
5. -42x
6,.' -X4 y 7
7. 72.x3y2 8. -64x12 9. -3.x9y7
10. X 14y 2 11. 8x l 2y3
Michigan
Page 45
A. x < 1 or x> 3
W. -4 s x s-1
T. -6 < x < 3
Y. x s -3 or x
A. -3sxs6
~
7
Page 50
1. (4,5)
D. -11 < x < 3
A. V2sxs2
data-way
1. yes
2. no
5. yes
3.
yes
6.
yes
8.
9.
no
yes
2.
(1, 8)
3.
(17,10)
4.
(3, 3)
5.
(3, -1)
6.
(-6, 8)
7.
(3,5)
8.
(3,4)
9.
(5, 2)
10. (12,1)
Page 46
4. no
7. no
Garfield the Cat
three days
For a tune-up!
Page 51
S.
10. yes
X.
(2, 1) M.
(-3, 2) I.
S.
(2,5)
E.
(1, 1)
(6,0)
(-3, -5)
L.
I.
(3, 10)
(-6, 8)
2.
1.
4.
y
7.
/
(0, 1) 5.
(-1, -1) 8.
3.
(4,0)
(2, -2)
6.
(2,3)
(4, -5)
9.
(3,7)
John Wayne
Page 53
1. (1, -%) 2.
7.
(1, 0)
(-3, 0)
seven gold
1
81 y 2
4.
6.
7.
(-4x)/(3 y 3)
8. -2 y 3
9.
9x6
thirty-six
1/(2x)
-3/(xy)
Page 60
1.
3.
2/x5
(2 y 3)/0
(-3 y 6)/x4
2. -3/y
4.
1/4
6.
8.
(-4 y 9)/x4
1
Seinfeld
(-3, 0)
x
4.
3.
5.
7.
Page 52
1. (-2, -2) 2.
'Page 47
2. -x/9
5. 80
six miles
six
Page 59
1. x
Page 61
1.
0.00031
2.
804,000
3.
0.0046
4.
2,000
5.
56,200,000
6.
(2,2)
(-7, 3)
6.
0.00000703
9.
(4,0)
7.
5.62 x 106
8.
7.8
(-5, 2)
3.
5.
(1, 1)
8.
(2,3)
X
10-6
18122010 Algebra Made Simple • © Carson-Dellosa
I
I