Name _ Date _

Dividing Monomials

18x6 y 18 x6 - 3 1 -6x3 -3x3 YS =--=J • -1-· r =7

1 .

2.

3.

4.

5.

6.

7.

8.

10 m-5 = m

3 2X y _ 2x2 y2 ­

34ab2a2 b 2 ­

27JJ '18Jv" =

13e9d 10

-26e9d =

3ft-3R=

-52x3V-z _ 13XV ­

8xy2 16x3 y5 =

9 .

10.

11.

12.

13.

14.

15.

16.

45x-= 5

18x2

y = 24xy

2 356s t4s 2 t =

48a3 be5

12a5 b 3 e 2 ­

25x2y _ -15XV ­

8m2 n 2

12m2 n 3 ­

4-17e5d -51ed 3 =

24x2 y3 Z4

-44X4 y3z2 =

Published by Instructional Fair, Copyright protected, Page 54 0-7424-1788-3 Algebra

Answer Key

From Factors to Equations 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.

EKompkt: II") and f ore the solutions, what was the equatIon?

1. Use the soIulk>ns 10 wrlle sImple equations equal to zero. x + I = 0 and 3x - 2 = 0

2. Use the expressions as foctors of on equaflon. (X+ 1) (3x- 2) =a 3. Expand the factored form. 3x2 - 2x+ 3x- 2 = 0 4. Simplify. 3x2+x-2=O

Use the gl....en solullons 10 write 9qu01lons. Shode the regions below containing the equations. I

6. x .. -;. "8

2. xc."7,"2I x+7=0 x+2=02: ~+7)(X+2j=O 3 +2x+7x+14=0 4: XZ+9X+14=O

I 4. x= 2' 3

1. 2x I = 0 x - 3 = 0

i ~tH;i=lJ 3

5. x .. - 4' 2

~. ~IN~&~;?:QQ ~: i~:ti±gW-Q

Three solutions mean three faelors.

r+2x+24::10

+ x-h. 0 I

The femolnlng letters spelllhe name of the type of equollon In problem 9: A CUBIC

r-9x-14=O

Dividing Monomials gII

~ 18 ",,-J 1 '61<' '3 =~·-1-·Y==7 II

mlO

(;5= m5 9. 5><' 5= I'

2. ~= X

2 10.

lax2 y 24xy =

3x 4

3, 40bJ

202b 2 = 2b 0

II. 56s't'4:S'If = 14r

4. 27J-J "I&Tv" =

3 ~

12. 4803bc5

1205b 3c 2 = 4c3

(lfl

5. 13c9d 1O

"26c"d '"' cf -2 13' ~= 'I

5x 3y

6. 3N "3H= -1 14.

6m2n2

12m2nJ = 2

3n

7, ~=I -4x2z 15. .17e'd' "Sled J =

c4d 3

8. 8xy'

l6x'Y" = 1

W 16. 24>~Z:='44 z

6l llX'

Dividing a Polynomial by a Monomial

r +6(+5 ={+~+~-(+6+~ ( (( ( (

0 2 +20 14k9 m) - 4k2m 'l + 12km3

=1. 0+2 9. a 2km 2

7~m - 2k+ 6m

14x + 35 12v'-27v' + 18u'?2. --7-= 2x+5 10.

3lN' .;- 9v4---+6

u u 4 y2 + 6y 2x' - IOxy

3. -2-y-= 2y+ 3 11. --2-x- x- 5y

Jx'y-xy' ,4. 12. 3x y' - 6x'r' + 6xy' - ; 2 2

xy x- Y 3xy - Y - XV + Y

25u2-15u-5 6z2-3z+95. 13, --3-z--= 2z-1+~'5

-5J + 3u+ 1 2

12x' - 9'" + 6><' 6Ql +420+ 72 1 7 126, 14,3x 60' Ci+c;+C14x- 3; +2;

m 2n2 +m_n 64><'-64-'"7. 15, mn ~= x-1

mn +.l. - 1. n m

44502b 4 - 6Odb2 -1502b 18m3n - 12m2n3 + 24n2

8. = 16. = "1502b 6m2n -383 + 40b+ 1 3mnJ -2n2+~

II

Simplifying Fractions

5x2 + 30x- 3S _ .6'(x + 7l-f!<:"1l _~ 5 - 5x2 - ;8"(X+ 1) U<--t'i ­ X+ 1

(56"II~

1.

2.

3.

4.

5,

6.

7.

8a-8b c;et;i =

x 2 +8x+16 ~=

12 ­ 40 0 2 +0-12 =

t 2 + 4t- 5 t 2 + 9t+ 20 =

z'l-4z-5 Z2+ 4Z -45=

6b J - 24b2

b 2+ b-20 =

-x' + 8x- 12 ~

8 o+b

x+4 x-4

-4 0+4

t- 1 t+ 4

z+ 1 z+ 9

6~

b+5

6-x

8,

9.

10.

11.

12,

13.

14.

203 + 0 2 -30 603 + 502 _ 60

x2-9

x2+x-6 =

3:<2+2x-1 ~=

:<2 + 5:< x2-25 =

0 2 _ 110 + 30

a 2 -90+18

2y' ­ 12y' + 2y y" -6y+ 1

a+b 0 2 + 2ab"+'t1 =

0-1 30-2

x-3 x-2

3x- 1 x+ 2

X

x-5

0-5 0-3

2y

1 o+b

Published by Instructional Fair. Copyright protected. 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.

21. x y R. 1 xy 2.x

-Q2y2. 18xy

10x2y3. T. x 10x2y

4. 13xy Y.~ 26x2y xy

(9y)35. x. 9x6

9y

-18xy26. 6x2y3

-1Q2y7. 9xy4

8. (-3.xy)(6x2y4) T. 81 y2

9x3y2

(3x2)3(2xy)9. I. 1 ......6xy

-1 2 3 4 5 6 7 8 9

( ... '···111.

a FS122010 Algebra Made Simple • © Carson-Dellosa I Dividing exponents ~

8. V=(4, -2), opens down 3. 4.

9. V =(5, 1), opens up

10. V =(3, -5), opens down

four

Page 43

T. x < 10 A. x ~ 19

I. x> -22 O. x> -2 5. 6.

A. x ~ 11 E. x < -14

L. x s 25 E. x <-8

H. x ~ 2 N. x> 47

H. x> -3 E. x~6

C. x> -6 N. x s-2

An ace in the hole!

Page 44 7. 8.

1. xs-2orx>8

2. 1 s x s 7

3. -10<x< 10

4. x < -7 or x ~ 8

5. -3 s x < 5

6. x < 2 or x> 5 9.7. x ~ 9 or x s 7

8. x < -3 or x ~ 5

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 ~ 7

A. -3sxs6 1. (4,5) 2. (1, 8) 3.

D. -11 < x < 3 4. (3, 3) 5. (3, -1) 6.

A. V2sxs2 7. (3,5) 8. (3,4) 9.

data-way

Page 54

1. Has many solutions

2. Has no solution

3. Has no solution

4. Has many solutions

5. Has no solution

6. Has many solutions

7. Has no solution y

8. Has no solution

9. Has many solutions III Bugs Bunny

Page 55

1. Quadrants I, II, III, IV

2. Quadrant II

3. Quadrants I, II, III

4. Quadrants I, III, IV

5. Quadrants I, II

6. Quadrant I

7. Quadrants I, IV

8. Quadrants II, III

Thriller (Michael Jackson)

Page 58

1. 30 2. 32x5 3. x15

4. 30x6 5. -42x7 6,.' -X4y7

7. 72.x3y2 8. -64x12 9. -3.x9y7

X1410. y2 11. 8x l 2y3

Garfield the Cat

Page 59

1. x 2. -x/9(17,10)

3. 1 4. 1/(2x)(-6, 8)

5. 81 y2 6. -3/(xy)(5, 2)

7. (-4x)/(3y3) 8. -2y3

y

10.

three days

Page 50

10. (12,1) For a tune-up! 9. 9x6 thirty-sixPage 46

Page 51 1. yes 2. no 3. yes Page 60

S. (2, 1) M. (1, 1) L. (3, 10) 4. no 5. yes 6. yes 1. 2/x5 2. -3/y

X. (-3, 2) I. (6,0) I. (-6, 8) 7. no 8. yes 9. no 3. (2y3)/0 4. 1/4

S. (2,5) E. (-3, -5) 10. yes 5. 80 6. (-4y9)/x4

six miles six 7. (-3y6)/x4 8. 1

Page 52 Seinfeld'Page 47 1. (-2, -2) 2. (-3, 0) 3. (4,0)

1. 2. Page 61 4. (0, 1) 5. (2, -2) 6. (2,3)y

1. 0.00031 7. (-1, -1) 8. (4, -5) 9. (3,7)

2. 804,000/ John Wayne

x 3. 0.0046 Page 53 4. 2,000 1. (1, -%) 2. (-5, 2) 3. (2,2) 5. 56,200,000 4. (1, 0) 5. (1, 1) 6. (-7, 3) 6. 0.00000703 7. (-3, 0) 8. (2,3) 9. (4,0) 7. 5.62 x 106

seven gold 8. 7.8 X 10-6

18122010 Algebra Made Simple • © Carson-Dellosa

I I