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Answers

Copyright © Big Ideas Learning, LLC Algebra 1 All rights reserved. Answers

A77

70. 5, 20%, 10.4a r y= = =

71. 1000, 0.2%, 1008a r y= = =

72. 1, 200%, 81a r y= = =

73. ( )20,000 1 0.15 , where yearst

y t= − =

74. ( )8 1 0.05 ,t

y = + where weekst =

75. ( )1,000,000 1 0.5 , where dayst

y t= − =

76. 3x = 77. 9x = − 78. 2x =

79. geometric 80. geometric 81. arithmetic

82. 18, 6, 2 83. 96, 192, 384 84. 9 9 9

, ,4 8 16

85. 1, 4, 7, 10, 13, 16 86. 3, 6, 12, 24, 48, 96

87. 1 11, 3n na a a −= =

Chapter 7 7.1 Start Thinking

Sample answer:

An expression showing the sum of all the terms above is 6 2 3 103 3 .b c m t+ + + +

7.1 Warm Up

1. 15− 2. 1 3. 52−

4. 38 5. 9− 6. 9−

7.1 Cumulative Review Warm Up

1. ( )7,1 2. ( )8, 5

3. ( )6,18− 4. ( )1,1

7.1 Practice A

1. 3 2. 5 3. 7

4. 34 5 2;h h− + − degree 3;= leading

coefficient 4;= − trinomial

5. 34 10;p + degree 3;= leading coefficient 4;=binomial

6. 76 ;v degree 7;= leading coefficient 6;=

monomial

7. The expression has 3 terms; 2

8. 3 4t + 9. 4 4v− −

10. 23 11 10j j− − + 11. 24 3w w+ +

12. 3 2p− + 13. 3w− −

14. 23 11y y− + + 15. 27 14 8b b− −

16. The negative sign should not distribute to 7x in the linear term in the second line.

( ) ( )

( ) ( ) ( )

3 3

3 3

3 3

3

8 2 3 7 6

8 2 3 7 6

3 8 7 2 6

4 8

x x x x

x x x x

x x x x

x x

− + + + +

= − + + + +

= + + − + + +

= − +

17. 2 22 2p pq q− − 18. 2 27 2 8x xy y− + +

19. no; subtracting x from ( )3 3 2x x x x− = does not

yield the same result as subtracting 3x from

( )3 2x x x x− = −

7.1 Practice B

1. 8 2. 7 3. 13

4. 5 210 8 3 ;t t t− + degree 5;= leading

coefficient 10,= trinomial

5. 4 223 ;

9n n nπ+ − degree 4;= leading

coefficient 3;= trinomial

6. 514 ;p degree 5;= leading coefficient 14;=monomial

7. trinomial; degree 5= 8. 210 3 2t t− − +

9. 213 9 4y y− + 10. 33 17k k− +

11. 3 25 5 6q q q− + + −

Object Letter How Many Expression

table t 3 3t

couch c 2 2c

light 3 3

balloon b 6 6b

movie m 103 103m

Answers

Algebra 1 Copyright © Big Ideas Learning, LLC Answers All rights reserved. A78

12. 3 25 4t t t− − +

13. 3 23 7 13w w w− − −

14. 4 25 8 4x x x+ − −

15. 3 217 6 6 10g g g− + − +

16. 53 w+ 17. 2 22 15g gh h− −

18. 2 22 8 9m mn n− − +

19. 216 25 4;t t− + + when 1, 13 ftt h= =

7.1 Enrichment and Extension

1. 5 12x + 2. 3 2x + 3. 18 22x +

4. 7 20x + 5. 7 10x + 6. 9 ft

7. 9 ft 8. 9 ft

9. 215 46 24x x+ + 10. 216 48 9x x+ +

11. 3x −

7.1 Puzzle Time

BY ITCH-HIKING

7.2 Start Thinking

Sample answer:

The answers to the first two expressions are the same, as are the answers to the last two expressions. The first two expressions are related because the second expression is an expanded form of the first expression where the first set of parentheses is broken into two terms and the Distributive Property is used on the second set of parentheses. The last two expressions are related in the same manner.

7.2 Warm Up

1. 16 48b + 2. 12 6x − 3. 16 28x− +

4. 32 12y− − 5. 12 24x y− − 6. 8 20x− +


1. As x increases by 1, y increases by 1. The rate of change is constant. So, the function is linear.

2. As x increases by 1, y is multiplied by 8. So, the function is exponential.

7.2 Practice A

1. 2 9 20x x+ + 2. 2 5 6x x− −

3. 2 9 14x x− + 4. 2 6 8y y+ +

5. 2 3 28q q− − 6. 22 5 3x x− +

7. The x is subtracted in the second factor, so the first column should be .x−

( )( )2 5x x− −

( )( ) 22 5 7 10x x x x− − = − + −

8. 2 11 18u u+ + 9. 2 30w w+ −

10. 2 7 8m m+ − 11. 2 9 18y y− +

12. 2 3

4q q− − 13. 25 37 14t t− +

14. 24 4 15x x+ − 15. 23 10 48x x+ −

16. 3 27 11 2x x x+ + + 17. 3 27 4 30y y y+ + −

18. 3 210 23 14h h h− + −

19. no; The degree of the product is the sum of the degree of the binomial and the degree of the trinomial.

7.2. Practice B

1. 2 13 40p p− + 2. 25 9 2t t− −

3. 24 25 21v v+ − 4. 210 18 4p p+ −

5. 221 34 8r r− + 6. 28 42 54t t− +

Expression x Answer

( )( )2 2x x− − 7 25

( ) ( )2 2 2x x x− − − 7 25

( )( )4 4z z+ − 7 33

( ) ( )4 4 4z z z− + − 7 33

− x 5

x 2x− 5x

2− 2x 10−

Answers


A79

7. The 5x term was added as a 25x term instead. ( )( )2 5x x− −

( )( ) 22 5 7 10x x x x− − = − + −

8. 2 72z z+ − 9. 2 2 8

5 25m m+ −

10. 23 20 32x x− + 11. 212 27g− +

12. 3 211 28p p p+ + 13. 3 27 10d d d− +

14. 21 93

2 2x x+ + 15. 2 11 24x x+ +

16. 3 23 35 48 20x x x+ + −

17. 3 26 13 78 35t t t− − −

18. 3 26 9 31 40r r r− + + −

19. Sample answer:

( )( )3 2 4 3 22 3 6x x x x x x+ − = − −


1. 24 12 9, 8 12A x x P x= + + = +

2. 2

2 , 3 62

xA x P x= + = +

3. 22 5 3, 6 4A x x P x= + − = +

4. 22x 5. 229x

6. 22 12 16x x+ +

7. 29

2

x 8. 224x

9. 25 17 6x x+ +

7.2 Puzzle Time

BY PASSING THE BUCK

7.3 Start Thinking

( )( ) 2 23 3 3 3 9 9;x x x x x x+ − = − + − = −

The result is only the two terms because the middle two terms cancel each other out; The first term in the answer is the square of the first term in each set of parentheses and the second term is the square of the second term in each set of parentheses.

Sample answer:

( )( ) 2 27 7 7 7 49 49;x x x x x x+ − = − + − = −

Yes, the previous explanation will hold true for any number;

3; Because the middle terms will not cancel out in the expressions ( )( )3 3x x+ + and ( )( )3 3 ,x x− − there

will be three terms in the answer: These expressions both feature duplicate factors, so they can be rewritten

as ( ) ( )2 23 and 3 ,x x+ − respectively.

7.3 Warm Up

1. 2 4 4x x− + 2. 2 7 18y y+ −

3. 2 8 12z z− + 4. 23 22 24x x+ +

5. 216 64 60x x− + 6. 2 212 27 6a ab b+ +


1. 13 4x − = 2. 5.5 2.5x − =

3. 10.5 5.5x − = 4. 3.5 6.5x − =

5. 1 4x + = 6. 0.5 1.5x + =

7.3 Practice A

1. 2 14 49x x+ + 2. 24 12 9w w− +

3. 216 16 4q q+ + 4. 2 16n −

5. 2 49v − 6. 225 4x −

7. 236 a− 8. 219

p− 9. 2 24x y−

10. ( )( )20 1 20 1 400 1 399− + = − =

11. ( )( )50 1 50 1 2500 1 2499− + = − =

12. ( )( )30 3 30 3 900 2 90 9 1089+ + = + • + =

5 − x

x 5x 2x−

2− 10− 2x

Answers


13. Only the first and last term of the square of a binomial pattern are present.

( ) ( )( )2 2 2

2

5 2 5 5

10 25

x x x

x x

− = − +

= − +

14. a. 2900 x−

b. 2864 ft ;A = The original room has the larger

area, 2900 ft .

15. 4 25x − 16. 8 44 4y y− +

7.3. Practice B

1. 236 36 9p p− + 2. 2 29 6c cd d− +

3. 2 225 20 4x xy y+ + 4. 281 16q−

5. 249

g− 6. 2 29 64m n−

7. 264 9u− 8. 2 81c −

9. 2 29 49s t−

10. ( )( )20 7 20 7 400 2 140 49 729+ + = + • + =

11. ( )( )1 1 12 2 4

14

40 40 1600 2 20

1640

+ + = + • +

=

12. ( )( ) 151 1 14 4 16 16

5 5 25 24+ − = − =

13. The constant term should be ( )( )5 5 25.− = −

( )( ) 2 2

2

5 5 5

25

x x x

x

+ − = −

= −

14. a. 240,000 400 x xπ π π− + b. 10,000π

15. 4 2 2 49 42 49x x y y+ +

16. 8 69z w− 17. 16k =

18. Sample answer: 10, 3; 4, 5a b a b= = = =


1. 23 8 4x xπ π π+ +

2. 23

4

xπ 3. 217 xπ

4. 3 2

3

x x yπ π+ 5. 3 212 8x xπ π+

6. 35 xπ 7. 390 xπ 8. 368

3

xπ

7.3 Puzzle Time

VANISHING CREAM

7.4 Start Thinking

The equation ( )( )3 5 0x x+ + = would be rewritten as

( )( ) 0;a b = The equation is equal to zero, so either

0 or 0a b= = must be true; This means that either

3x + is equal to zero or 5x + is equal to zero; The two resulting equations are 3 0 and 5 0.x x+ = + = The solutions are 3 and 5;x x= − = − The solutions

are the numbers that can be put into the original equation to make the equation true.

7.4 Warm Up

1. 13x = − 2. 6x = −

3. 32x = − 4. 27x =

5. 33x = 6. 12x =


1. 2t < −

2. 12z ≤

3. 8n ≥ −

4. 15m >

5. 2f ≤

6. 44t ≥

7.4 Practice A

1. 0 and 5x x= = 2. 0 and 8d d= = −

20−4 −2−6

1511

12

1397 17

−4−8 −6−10−12

1915 171311

62 40−2

4844 464240

Answers


A81

3. 0 and 7t t= = − 4. 2 and 5x x= − =

5. 1

3 and 5

p p= − = − 6. 2

3q = −

7. 10y =

8. 0, 4, and 5t t t= = − =

9. 5

0, 9, and2

u u u= = =

10. 5 and 5x x= = − 11. 2 and 4x x= = −

12. ( )4 3t t + 13. ( )25 2 3k k −

14. ( )24 2 5x x − 15. 1

0 and3

t t= =

16. 0 and 2y y= = − 17. 7

0 and 4

n n= = −

18. The second term of the polynomial was lost when factoring in the second step.

( )

215 5 0

5 3 1 0

t t

t t

+ =

+ =

5 0 and 3 1 0

10 and

3

t t

t t

= + =

= = −

19. 1

0 and ;4

x x= = times when frog jumped and

landed.

7.4. Practice B

1. 0 and 4y y= = 2. 6 and 1d d= = −

3. 3 and 5w w= − = 4. 2 2

and3 3

x x= = −

5. 2

0, 4, and3

h h h= = = −

6. 0 and 2k k= = − 7. 7 and 9y y= = −

8. 5

3, , and 23

n n n= = =

9. 5, 6, and 4n n n= = =

10. 11 and 6x x= = − 11. 24 and 14x x= = −

12. ( )12 3 2v v + 13. ( )5 3 2r r −

14. ( )46 3 2a a + 15. 1

0 and2

h h= =

16. 0 and 3w w= = 17. 0 and 4n n= = −

18. The Zero-Product Property was used incorrectly by not first rewriting the equation to make the right side equal to zero.

( )

2

2

15 5

15 5 0

5 3 1 0

5 0 and 3 1 0

10 and

3

t t

t t

t t

t t

t t

=

− =

− =

= − =

= =

19. Sample answer: ( )( )22 5 2 0;x x− − = yes,

( ) ( )22 5 2 0x x− − =


1. 8

61

xx

+ +−

2. 31

2 74

xx

+ +−

3. 6

23

xx

− −−

4. 5x +

5. 19

2 62 3

xx

+ ++

6. 5

33

xx

− ++

7. 2 93 2

2x x

x+ + +

− 8. 2 21

2 92

x xx

+ + +−

7.4 Puzzle Time

HORSE THAT WAS SO SLOW DURING A RACE THAT THE JOCKEY KEPT A DIARY OF THE TRIP

Answers


7.5 Start Thinking

The sum of the constant terms from each set of parentheses is the coefficient of the x-term in the standard form of the polynomial. Likewise, the product of the constant terms from each set of parentheses is the constant term in the standard form of the polynomial.

7.5 Warm Up

1. 1, 2, 3, 6, 7, 14, 21, 42

2. 1, 2, 3, 6, 17, 34, 51, 102

3. 1, 2, 4, 7, 14, 28 4. 1, 2, 4, 7, 8, 14, 28, 56

5. 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

6. 1, 2, 3, 4, 6, 9, 12, 18, 36


1. nonlinear; You cannot rewrite the equation 2 14y x= − in y mx b= + form, due to the

quadratic term 2.x

2. linear; You can rewrite the equation 8y x= +

in y mx b= + form, with 1m = and 8.b =

7.5 Practice A

1. ( )( )2 3x x+ + 2. ( )( )6 2x x+ +

3. ( )( )4 7z z+ + 4. ( )( )3 4w w− −

5. ( )( )2 12y y− − 6. ( )( )4 7x x− −

7. ( )( )5 4x x+ − 8. ( )( )2 8y y+ −

9. ( )( )9 1m m+ − 10. ( )( )5 8n n+ −

11. ( )( )8 3d d+ − 12. ( )( )7 4z z+ −

13. a. 8x − b. 16 ft

14. Although ( )( )3 6 18,− − = the cross-terms sum to

6 3 9 ,x x x− − = − not 11x− as desired.

( )( )2 11 18 2 9x x x x− + = − −

15. length 15 ft, width 3 ft= =

16. base 14 cm, height 5 cm= =

17. 2 5 24 0;x x− − = If 3x = − is a solution, then

( )3x + is a factor. If 8x = is a solution, then

( )8x − is a factor. So, the equation must be

( )( )3 8 .x x+ −

7.5 Practice B

1. ( )( )4 1x x+ + 2. ( )( )7 2w w+ +

3. ( )( )12 3y y+ + 4. ( )( )5 9x x− −

5. ( )( )3 13j j− − 6. ( )( )9 10m m− −

7. ( )( )7 5y y+ − 8. ( )( )2 10w w+ −

9. ( )( )5 6b b+ − 10. ( )( )3 9p p+ −

11. ( )( )7 8q q− + 12. ( )( )9 4t t+ −

13. Although ( )( )12 8 96,− = − the cross-terms sum to

12 8 4 ,x x x− + = − not 4x as desired.

( )( )2 4 96 12 8x x x x+ − = + −

14. base 20 m, height 12 m= =

15. length 11 cm, width 5 cm= =

16. a. The zeros of the polynomial correspond to its factors.

b. ( )( )4 2x x− +


1. ( )( )3 1 2x y+ − 2. ( )( )4 5 3b c a c− −

3. ( )( )25 6 5 1y y+ +

Standard Form

Factored Form

Sum of Constant

Terms

Product of Constant

Terms

2 8 12x x+ + ( )( )

6

2

x

x

+ •

+ 8 12

2 7 12x x− + ( )( )

4

3

x

x

− •

− 7− 12

2 2 15x x− − ( )( )

3

5

x

x

+ •

− 2− 15−

2 2 24x x+ − ( )( )

6

4

x

x

+ •

− 2 24−

Answers


A83

4. ( )( )22 2 5 3 1x x− +

5. ( )( )24 1 4v v+ − 6. ( )( )5 1 3 2xy x y− −

7. ( )( )4 5 4y x z p− + 8. ( )( )4 3 4 3x y x+ +

9. ( ) ( )212 15 4 5 3 4 5 4 5xy x y y x y y y− − + = − − −

10. ( ) ( )22 3 6 9 2 3 3 2 3x x x x x x− − + = − − −

11. Sample answer:

( )( )( ) ( )

37 2 2 14 14

2 7 2 ;

x x x x x

x x x

− + = + − −

= + − +

Yes, the product of two binomials can always be factored again by grouping.

12. Exercise 9 has four terms, whereas Exercise 10 has three terms after simplification because with only one variable, like terms can be combined.

7.5 Puzzle Time

A FROG ON A COLD DAY

7.6 Start Thinking

Sample answer:

The list of factors is used to find the coefficient of the x-term in the standard form of each polynomial. To do this, multiply pairs of factors, choosing one set from each list, and then add the products to get the coefficient of the x-term.

7.6 Warm Up

1. ( )25 1x x− − 2. ( )2 12 4x x x− − +

3. ( )24 24 2z z− − 4. ( )23 27 12 1y y+ −

5. ( )27 10 11y x x+ + 6. ( )215 3 6t t− +


1. 2 17y x= − + 2. 2 16y x= −

7.6 Practice A

1. ( )( )6 3 1x x− + 2. ( )( )5 2 5x x+ −

3. ( )( )9 1 3x x− − 4. ( )( )2 2 1x x+ −

5. ( )( )3 4 2 5x x+ − 6. ( )( )3 2 1x x− +

7. ( )( )6 4 3x x+ − 8. ( )( )9 2 5x x− +

9. ( )( )8 3 2x x+ − 10. ( )( )2 3 2p p− + −

11. ( )( )5 1 6v v− + − 12. ( )( )2 1 3 4v v− − +

13. Neither factor has a negative t-term, which is necessary to make the leading coefficient negative.

( )( )22 13 15 2 3 5t t t t− + − = − + −

14. 2 and 3x x= − = 15. 7and 4

3p p= − =

16. 3

, 42

x = 17. 3, 2x = −

18. 13sec

8t =

19. 18, 21, 24, 42, 81t = ± ± ± ± ±

20. ( )( )3 2 5a b a b+ − 21. ( )( )4 3x y x y− +

7.6 Practice B

1. ( )( )5 2 3x x+ − 2. ( )( )8 6 4x x− +

3. ( )( )6 1 7x x+ + 4. ( )( )2 1 9x x− +

5. ( )( )4 5 3 2p p− + 6. ( )( )2 2 5 2w w+ +

7. ( )( )3 7 2y y+ − 8. ( )( )6 1 2 5j j− −

9. ( )( )3 5 5 3d d+ − 10. ( )( )9 4 2v v− − +

11. ( )( )7 3 2 1m m− + − 12. ( )( )10 3 2 5q q− + −

13. The product of the binomials on the right side has a constant term of 2,− instead of 2.

( )2 26 4 2 2 3 2 1x x x x− + = − +

14. 3 1

and2 6

w w= = 15. 2 1

and9 2

t t= − =

16. 1

, 55

x = 17. 1

, 73

x = −

18. width 14, length 20= =

19. 25, 31, 35, 53, 77, 151t = ± ± ± ± ± ±

20. ( )( )5 2 2 3r s r s− + + 21. ( )( )4 3 5x x y x y+ −

Answers



1. ( )( )2 3 3 1x x+ + 2. ( )( )2 5 2 1y y+ +

3. ( )( )3 7 1p p+ − 4. ( )( )2 11 2 1x x− +

5. ( )( )3 1 4 1x x− + 6. ( )( )4 1 10 3v v− −

7. ( )( )4 15 2 1u u+ + 8. ( )( )3 4 3 1d d− + −

9. ( )( )15 3 1 2x x+ + 10. ( )( )2 1 1t t− − +

11. Sample answer:

( )( )28 10 3 2 3 4 1x x x x− − = − +

7.6 Puzzle Time

WITH A SAND DOLLAR

7.7 Start Thinking 2 2 216 4 ;x x− = − The factored form ( )( )4 4x x+ −

is equivalent to the original expression because when multiplied out, the middle terms cancel, leaving

2 16;x − ( ) ( ) ( )21 1 1 ;x x x+ = + +

( )( ) ( )22 8 16 4 4 4x x x x x+ + = + + = +

7.7 Warm Up

1. 2 10 25y y− + 2. 2 2 1x x+ +

3. 29 42 49x x− + 4. 2 24 4x xy y− +

5. 2 216 72 81x xy y− + 6. 24 28 49x x− +


1. ( )2,1 2. ( )2, 4

3. ( )1, 5 4. ( )2, 0

7.7 Practice A

1. ( )( )6 6x x+ − 2. ( )( )7 2 7 2t t+ −

3. ( )( )1 5 1 5y y+ − 4. ( )( )11 8 11 8 57− + =

5. ( )( )17 15 17 15 64− + =

6. ( )( )65 62 65 62 381− + =

7. ( )27k + 8. ( )2

9m − 9. ( )217x +

10. a. 3x + b. 28 cm

11. 5v = ± 12. 4p = −

13. 7q = 14. 5

4x = ±

15. ( )( )5 2 2x x+ − 16. ( )24 3x −

17. ( )29 5x + 18. 1 sec

19. a. cannot be factored; ( )22 12 36 6p p p+ + = +

b. cannot be factored; ( )22 16 64 8x x x− + = −

20. a. 2 23x −

b. 8 in.; 2 9 55, 8x x− = =

7.7 Practice B

1. ( )( )10 7 10 7x x+ −

2. ( )( )11 5 11 5s t s t+ −

3. ( )( )12 12x y x y+ −

4. ( )( )86 84 86 84 340− + =

5. ( )( )44 39 44 39 415− + =

6. ( )( )28 27 28 27 55− + =

7. ( )213z + 8. ( )2

4 5x − 9. ( )29 2a +

10. a. 5 4x +

b. no; 60 64<

11. 9

10x = ± 12. 12w = −

13. 9s = 14. 1

6y =

15. ( )( )8 3 3y y+ − 16. ( )27 4p +

17. ( )23 4 3t − 18. 1.5 sec

19. a. cannot be factored; 2

2 1 1 1

2 16 4q q q

+ + = +

b. cannot be factored; 24 28 49x x+ + =( )22 7x +

Answers


A85

20. a. 2 26x − b. 10 in.; 2 36 64, 10x x− = =


1. 5 4 3 2 2 3 4 55 10 10 5x x y x y x y xy y− + − + −

2. 3 2 2 36 12 8a a b ab b+ + +

3. 4 3 2 2 3 416 96 256 256x x y x y xy y+ + + +

4. 5 4 3 2 2 3 4 515 90 270 405 243a a c a c a c ac c− + − + −

5. 6 5 4 2 3 3 2 4 5 66 15 20 15 6a a b a b a b a b ab b− + − + − +

6. 8 6 4 212 54 108 81x x x x+ + + +

7. 320x y 8. 14144a

7.7 Puzzle Time

IN THE DICTIONARY

7.8 Start Thinking

yes; It is common to encounter a polynomial containing a GCF that can be factored out, leaving a trinomial that may be factored using one of the other techniques listed in the table.

7.8 Warm Up

1. 60 2. 210 3. 18

4. 270 5. 240 6. 25


1. 2 2. 9 3. 8

4. 4 5. 256 6. 6

7.8 Practice A

1. ( )( )2 1 3x x+ − 2. ( )( )2 9 2x x+ −

3. ( )( )22 3 1y y+ −

4. ( )( )( )2 2 3 5p p p+ − +

5. ( )( )4 3 3y y y+ − 6. not factorable

7. ( )23 2t t + 8. ( )( )2 3 1 5q q q− + −

9. ( )( )35 1 2y y y+ − 10. ( )27 3 1x x+ +

11. 0, 5, 2j = − − 12. 0, 6w = ±

13. 2, 3y = ± 14. 0, 7, 6t = −

15. 0, 7x = ± 16. 0, 2, 5x =

17. a. 26 9V x x= −

b. 5cm 7 cm 3cm× ×

18. ( )( )( )3 2 2a b a a+ + −

19. ( )( )( )2 3 1 3 1g h g g− + −

7.8 Practice B

1. ( )( )3a b a+ − 2. ( )( )2 7m m n+ +

3. ( )( )4t t v− + 4. ( )( )3 3 4x y x+ −

5. ( )( )25 3 2 3 2y y y+ − 6. ( )238 3w w −

7. ( )( )( )4 4 3p p p+ − − 8. ( )26 2 7z z− +

9. ( )( )27 3 1 4h h h− + − 10. ( )( )( )7 7 2x x x+ − +

11. 2, 3p = − ± 12. 0, 5, 8y = −

13. 0, 3t = ± 14. 5, 3

3q = ±

15. 0, 3x = 16. 50, 4,

3x = −

17. a. 3 29 3V x x= −

b. 3 in. 9 in. 8 in.× ×

18. ( )( )5 2 7x x y− + 19. ( )( )2 3 5p q p q− +


1. ( )( )3 36 5x x+ +

Polynomial GCF 2

++

x bxc

2 ++

ax bxc

Differenceof

Squares 28 20

48

x x++

√

2 19

48

x x−+

√

2 16x − √

26 19

8

x x++

√

Answers


2. ( )( )( )( )1 1 2 2y y y y− + − +

3. ( )( )4 43 2 2p p− +

4. ( )( )( )22 1 2 1 1x x x− + +

5. ( ) ( )2 21 1x x− + 6. ( )( )5 52 5x x− + +

7. ( )( )3 32 1 4 3u u+ + 8. ( )( )3 37 2d d− −

9. ( )( )( )4 2 22 1 2 2t t t− + − +

10. ( )( )( )( )2 41 1 1 1x x x x− + + +

7.8 Puzzle Time

VERY COOL ANSWERS

Cumulative Review

1. 2w = 2. 5t π= 3. 1x = −

4. 9 13x− < <

5. not possible

6. 1 or 3x x< >

7. a. 690 6x − ≤

b. 684 696x≤ ≤

8.

9.

10.

11. ( )1 7 5y x− = − − 12. ( )12 4

5y x− = +

13. ( )1 7y x+ = − + 14. ( )9, 5

15. ( )1, 1− − 16. ( )4, 3− 17. 5 and 8

18. a. 5000 100 2000w≤ +

b. 30 weeks

19. 8

2

8z

x 20.

3 6

1000

r z 21.

4

2

7z

x

22. 8 23. 1 24. 7−

25. 36 26. 27 27. 2187

28. 4.7% 29. 3.7% 30. 1

8

31. 2− 32. 1

75

33. ( ) ( )2000 1 0.40 ,t

f t = − where t is in years

34. ( ) ( )2500 1 0.035 ,t

f t = + where t is in years

35. ( ) ( )900 1 0.12 ,t

f t = − where t is in years

36. 6x = 37. 3−

38. 4x = 39. 824, 8,

3

40. 16, 32, 64 41. 3 3

3, ,2 4

42. 2, 0, 2, 4, 6, 8− − − −

43. 4, 28, 196, 1372, 9604, 67,228

44. 3 212 7 ;x x− + binomial

45. 7 416 3 7 ;w w w− + trinomial

−12 128−8

−9 13

40−4−16 16

4

31

0 2−2−4 6

x

y

2

−2

2−2

x

y

2

−2

−2

x

y

2

−2

−2 2

Answers


A87

46. 8 3 238 ;

8z z zπ− + + trinomial

47. 2 3g + 48. 3 5h− −

49. 2 11 17v v− + − 50. 3 212 5 5 7t t t− + − +

51. 2 15x− − 52. 13 38y +

53. 2 7 17x x− + −

54. 4 27 3 10 7w w w− − −

55. 2 2 15x x− − 56. 2 3 10y y− −

57. 2 13 30n n− + 58. 22 13 45r r+ −

59. a. 22 25 50x x+ +

b. 875 ft2

60. 2 8 16x x+ + 61. 29 30 25y y− +

62. 2 249 42 9x xy y+ + 63. 2 4w −

64. 24 16 16m m− + 65. 2 281 4h t−

66. a. 29 12 4x x+ +

b. 121 square units

67. 5, 3− 68. 5, 2−

69. 8

7 70.

2 2,

5 5−

71. 0, 3 72. 2

, 03

−

73. 0, 3 74. ( )( )2 5y y+ +

75. ( )( )4 2x x+ + 76. ( )( )9 2w w+ +

77. ( )( )4 2x x− − 78. ( )( )3 4d d− −

79. ( )( )10 2z z− − 80. ( )( )5 3m m+ −

81. ( )( )6 4z z+ − 82. ( )( )11 1x x− +

83. 4, 1− − 84. 6, 9−

85. ( )( )2 5 6x x+ + 86. ( )( )5 1 4y y+ +

87. ( )( )6 10 1w w+ + 88. ( )( )2 1 2t t+ +

89. ( )( )3 2 2u u− − 90. ( )( )2 5 3 5z z− + +

91. ( )( )4 4 1x x− − 92. ( )( )7 4 7r r− −

93. ( )( )5 3 3g g− − 94. 5 sec

95. ( )( )10 10x x+ − 96. ( )( )6 6h h+ −

97. ( )( )3 5 3 5b b+ − 98. ( )24k +

99. ( )215a − 100. ( )2

10 9g +

101. 8, 8−

102. 7, 7 repeated root

103. ( )( )25 6 5 1x x+ +

104. ( )( )24 3 7 4y y− +

105. ( )( )28 1 8w w+ −

106. ( )( )23 2 5 7x x− +

Chapter 8 8.1 Start Thinking

Sample answer:

The value of the coefficient of the 2x -term determines how wide or narrow the graph is, and if negative, shows a reflection in the x-axis; Sample answer: The graph of

2y x= − looks the most different because it is

reflected in the y-axis.

Quadratic equation Shape

Relationship to 2=y x

22y x= U-Shape slightly

narrowed

21

2y x= U-Shape slightly widened

2y x= − upside-down U-Shape

reflection in the x-axis

( )22y x= U-Shape

moderately narrowed

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