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Match the trinomial with its correct factorization.

1. x2 2 25 2. x2 1 10x 1 25 3. x2 2 10x 1 25

A. (x 1 5)2 B. (x 2 5)(x 1 5) C. (x 2 5)2

Factor the difference of two squares.

4. x2 2 1 5. b2 2 81 6. m2 2 100

7. p2 2 225 8. 4y2 2 1 9. 16n2 2 25

10. 9w2 2 100 11. 64z2 2 36 12. 49d2 2 25

13. 4r2 2 121 14. 9s2 2 144 15. c2 2 625

Factor the perfect square trinomial.

16. x2 1 6x 1 9 17. b2 1 10b 1 25 18. w2 2 12w 1 36

19. m2 2 8m 1 16 20. r2 2 20r 1 100 21. z2 1 16z 1 64

22. s2 1 22s 1 121 23. x2 2 16x 1 64 24. 4c2 1 4c 1 1

25. 16d2 1 8d 1 1 26. 9y2 2 6y 1 1 27. 9p2 2 12p 1 4

Solve the equation.

28. x2 2 9 5 0 29. p2 1 14p 1 49 5 0 30. d2 2 10d 1 25 5 0

31. 25m2 2 1 5 0 32. r2 2 2r 1 1 5 0 33. n2 1 20n 1 100 5 0

34. 4y2 2 9 5 0 35. 36x2 2 64 5 0 36. w2 1 4w 1 4 5 0

37. Washers Washers are available in many different sizes.

x

y

a. Write and factor an expression for the area of one side of the washer. Leave your answer in terms of π.

b. Find the area of one side of the washer when x 5 8 centimeters and y 5 3 centimeters.

38. Cherry Tree A cherry falls from a tree branch that is 9 feet above the ground.

a. How far above the ground is the cherry after 0.2 second?

b. After how many seconds does the cherry reach the ground?

39. Wind Chime A wind chime falls from a roof that is 10 feet above the ground.

a. How far above the ground is the wind chime after 0.5 second?

b. After how many seconds does the wind chime reach the ground?

Practice AFor use with the lesson “Factor Special Products”

Algebra 1Chapter Resource Book8-74

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Lesson Factor ax2 1 bx 1 c, continued

Study Guide

1. (7a 2 1)(a 2 7) 2. (2b 2 5)(2b 1 1)

3. (6c 2 7)(c 1 2) 4. 2(3r 1 4)(r 1 1)

5. 2(3s 1 4)(s 2 4) 6. 2(4t 2 1)(2t 2 1)

Problem Solving Workshop: Using Alternative Methods

1. 2.75 seconds 2. The linear term should be positive in the vertical motion equation. The diver enters the water after 2.75 seconds. 3. 1.5 seconds 4. 1 second 5. 2 seconds

Challenge Practice

1. (2y1/3 1 1)(2y1/3 1 5) 2. (4y2 1 1)(2y2 2 3)

3. 1 3 } y 1 1 2 1 3 }

y 2 5 2 4. 1 7 3 Ï

}

y 1 1 2 1 5 3 Ï}

y 1 1 2

5. 1 2 Ï}

y 2 3 2 1 2 Ï}

y 1 1 2 6. x 5 3 Î}

2 2 } 3 , 3

Î}

1 }

2

7. x 5 2 Î}

5 }

3 , Î}

5 }

3 8. x 5 2

1 } 5 , 2

5 } 3 9. x 5

49 }

9

10. x 5 2 2 Ï

} 5 } 5 ,

2 Ï}

5 } 5

Lesson Factor Special Products

Teaching Guide

1. x2 2 1; x2 2 25; 4y2 2 9

2. They are all binomials and both terms are perfect squares. 3. The first term of the product is the square of the first two terms of the binomials. 4. The second term of the product is the square of the last two terms of the binomials.

5. a2 2 b2 = (a 1 b)(a 2 b)

Practice Level A

1. B 2. A 3. C 4. (x 2 1)(x 1 1)

5. (b 2 9)(b 1 9) 6. (m 2 10)(m 1 10)

7. (p 2 15)(p 1 15) 8. (2y 2 1)(2y 1 1)

9. (4n 2 5)(4n 1 5) 10. (3w 2 10)(3w 1 10)

11. (8z 2 6)(8z 1 6) 12. (7d 2 5)(7d 1 5)

13. (2r 2 11)(2r 1 11) 14. (3s 2 12)(3s 1 12)

15. (c 2 25)(c 1 25) 16. (x 1 3)2 17. (b 1 5)2

18. (w 2 6)2 19. (m 2 4)2 20. (r 2 10)2

21. (z 1 8)2 22. (s 1 11)2 23. (x 2 8)2

24. (2c 1 1)2 25. (4d 1 1)2 26. (3y 2 1)2

27. (3p 2 2)2 28. 23, 3 29. 27 30. 5

31. 2 1 } 5 ,

1 } 5 32. 1 33. 210 34. 2

3 } 2 ,

3 }

2

35. 2 4 } 3 ,

4 }

3 36. 22 37. a. π(x 2 y)(x 1 y)

b. 55π cm2 38. a. 8.36 ft b. about 0.79 sec

39. a. 6 ft b. Î}

5 }

8 sec

Practice Level B

1. (x 2 6)(x 1 6) 2. (5p 2 12)(5p 1 12)

3. 4(b 2 5)(b 1 5) 4. 9(2m 2 3)(2m 1 3)

5. 22(x 2 4)(x 1 4) 6. 24(r 2 5s)(r 1 5s)

7. (y 1 12)2 8. (3c 1 4)2 9. (5w 2 2)2

10. (4n 2 7)2 11. 22(3a 1 1)2 12. 5(2z 2 7)2

13. 27 14. 2 5 } 2 ,

5 }

2 15.

1 }

8 16. 23, 3 17. 25

18. 4 19. 25, 5 20. 10 21. 1 }

2 22. 2

5 } 3

23. 2 3 } 5 24. 2

3 } 8 ,

3 }

8 25. 8 26. 3 27. 1 sec

28. a. 0; 3.75; 5; 3.75; 0 b. Any other values between 0 and 20 because the ladder is on the ground at x 5 0 and meets the ground again at x 5 20. c.

0012345

5 10 15 20Distance from left end (feet)

Hei

gh

t (f

eet)

x

y

d. 10 ft

Practice Level C

1. (5x 2 9)(5x 1 9) 2. 25(3p 2 2)(3p 1 2)

3. (11w 2 25)(11w 1 25) 4. 4(3m 2 4)(3m 1 4)

5. 1 }

16 (3r 2 1)(3r 1 1) 6. (9x 2 7y)(9x 1 7y)

7. 23(y 1 8)2 8. 4(n 2 5)2 9. 3(2z 1 1)2 10. 6(2a 2 5b)2 11. 22(3s 1 4t)2

12. 1 } 5 (5z 1 1)2 or 5(z +

1 } 5 )2 13. 2

8 } 5 ,

8 } 5

14. 29 15. 2 7 } 2 ,

7 }

2 16. 10 17.

11 }

6 18.

4 }

15

19. 2 3 } 5 20. 4 }

7 21. 22, 2 22.

8 }

3

23. 2 1 } 5 24.

3 }

4 25. 90

26. 140 27. 36 28. 16 29. 9 30. 28

Algebra 1Chapter Resource Book A19

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