Algebra I Chapter 8

Solve each equation. Check the solutions.24. 3 x 2 + 24x + 48 = 0 25. 7 r 2 = 70r - 17526. 49 a 2 + 16 = 56a 27. 18 y 2 + 24y + 8 = 028. y 2 - _ 2 3 y + _ 1 9 = 0 29. a 2 + _ 4 5 a + _ 425 = 030. x 2 + 10x + 25 = 81 31. (w + 3 ) 2 = 232. p 2 + 2p + 1 = 6 33. x 2 - 12x + 36 = 1134. FORESTRY The number of board feet B that a log will yield can be estimatedby using the formula B = L _16 (D 2 - 8D + 16), where D is the diameter ininches and L is the log length in feet. For logs that are 16 feet long, whatdiameter will yield approximately 256 board feet?Real-World LinkSome amusement parkfree-fall rides can seat4 passengers across percoach and reach speedsof up to 62 miles perhour.Source: pgathrills.comFREE-FALL RIDE For Exercises 35 and 36, use the following information.The height h in feet of a car above the exit ramp of an amusement park’s free-fallride can be modeled by h = -16 t 2 + s, where t is the time in seconds after thecar drops and s is the starting height of the car in feet.35. How high above the car’s exit ramp should the ride’s designer start the dropin order for riders to experience free fall for at least 3 seconds?36. Approximately how long will riders be in free fall if their starting height is160 feet above the exit ramp?37. HUMAN CANNONBALL A circusacrobat is shot out of a cannonwith an initial upward velocityof 64 feet per second. If theacrobat leaves the cannon6 feet above the ground, willhe reach a height of 70 feet? Ifso, how long will it take him toreach that height? Use themodel for vertical motion.6 ft70 ftFactor each polynomial, if possible. If the polynomial cannot be factored,write prime.38. 4 a 3 + 3 a 2 b 2 + 8a + 6 b 2 39. 5 a 2 + 7a + 6 b 2 - 4b40. x 2 y 2 - y 2 - z 2 + x 2 z 2 41. 4 m 4 n + 6 m 3 n - 16 m 2 n 2 2- 24m nPRACTICEEXTRASee pages 734, 751.Self-Check Quiz atca.algebra1.comH.O.T. Problems42. GEOMETRY The volume of a rectangular prism is x 3 y - 63 y 2 + 7 x 2 - 9x y3cubic meters. Find the dimensions of the prism if they can be represented bybinomials with integral coefficients.43. GEOMETRY If the area of the squareshown is 16 x 2 - 56x + 49 squareinches, what is the area of therectangle in terms of x?44. REASONING Determine whether the following statement is sometimes, always,or never true. Explain your reasoning.a 2 - 2ab - b 2 = (a - b ) 2 , b ≠ 0Lesson 8-6 Perfect Squares and Factoring 459

45. OPEN ENDED Create a polynomial that requires at least two different factoringtechniques to factor it completely. Then factor the polynomial completely,describing the techniques that were used.46. Which One Doesn’t Belong? Identify the trinomial that does not belong with theother three. Explain your reasoning.4 x 2 - 36x + 81 25 x 2 + 10x + 1 4 x 2 + 10x + 4 9 x 2 - 24x + 16CHALLENGE Determine all values of k that make each of the following aperfect square trinomial.47. 4 x 2 + kx + 1 48. x 2 - 18x + k 49. x 2 + 20x + k50. Writing in Math Use the information about the project on page 454 toexplain how factoring can be used to design a pavilion. Explain how theequation (8 + 2x ) 2 = 144 models the given situation, solve this equation, andinterpret its solutions.51. What are the solutions for theequation 3(5x - 1 ) 2 = 27?A - 9 _5 and 2B -2 and _ 9 5C -_2 5 and _ 4 5D -_1 5 and _ 3 552. REVIEW Marta has a bag of 8 marbles.There are 3 red marbles, 2 bluemarbles, 2 white marbles, and 1 blackmarble. If she picks one marblewithout looking, what is theprobability that it is either blackor white?F1_8G _ 1 4H _ 3 8J5_8Solve each equation. Check the solutions. (Lessons 8-4 and 8-5)53. 9 x 2 - 16 = 0 54. 49 m 2 = 81 55. 8 k 2 + 22k - 6 = 0 56. 12 w 2 + 23x = -5Solve each inequality. Check the solution. (Lesson 6-2)57. _ r 5 > -11 58. 8 > _ 2 n 59. 76 < 4t 60. -14c ≤ 84361. BUSINESS Jake’s Garage charges $180 for a two-hour repair job and $375 for a five-hourrepair job. Write a linear equation that Jake can use to bill customers for repair jobs of anylength of time. (Lesson 4-3)62. MODEL TRAINS One of the most popular sizes of model trains is called the HO. Everydimension of the HO model measures _ 1 times that of a real engine. The HO model87of a modern diesel locomotive is about 8 inches long. About how many feet long is thereal locomotive? (Lesson 3-6)460 **Chapter** 8 Factoring

- Page 2 and 3: GET READY for Chapter 8Diagnose Rea
- Page 4 and 5: Method 2 Use a factor tree.Animatio
- Page 6 and 7: HELPHOMEWORKFor SeeExercises Exampl
- Page 8 and 9: EXPLORE8-2Algebra LabFactoring Usin
- Page 10 and 11: 2b. 18c d + 12 c 2 d + 9cd18c d 2 =
- Page 12 and 13: CommonMisconceptionYou may be tempt
- Page 14 and 15: 41. OPEN ENDED Write an equation th
- Page 16 and 17: Step 3 Arrange the 1-tilesinto a 1-
- Page 18 and 19: EXAMPLEb and c are PositiveFactor x
- Page 20 and 21: Solve a Real-World Problem by Facto
- Page 22 and 23: 43. FIND THE ERROR Peter and Aleta
- Page 24 and 25: 8-4Factoring Trinomials:ax 2 + bx +
- Page 26 and 27: A polynomial that cannot be written
- Page 28 and 29: HELPHOMEWORKFor SeeExercises Exampl
- Page 30 and 31: 8-5 Factoring Differencesof Squares
- Page 32 and 33: EXAMPLEApply Several Different Fact
- Page 34 and 35: HELPHOMEWORKFor SeeExercises Exampl
- Page 36 and 37: ProofsStandard 25.1 Students use pr
- Page 38 and 39: Factoring Perfect Square Trinomials
- Page 40 and 41: Reading MathSquare RootSolutions ±
- Page 44 and 45: CHAPTER8Study Guideand ReviewDownlo
- Page 46 and 47: Mixed Problem SolvingFor mixed prob
- Page 48 and 49: CHAPTER8Practice TestFactor each mo
- Page 50: More CaliforniaStandards PracticeFo