Algebra I Chapter 8

43. FIND THE ERROR Peter and Aleta are solving x 2 + 2x = 15. Who is correct?Explain your reasoning.Peterx 2 + 2x = 15x(x + 2) = 15x = 15 or x + 2 = 15x = 13Aleta2x + 2x = 15x 2 + 2x - 15 = 0(x - 3)(x + 5) = 0x - 3 = 0 or x + 5 = 0x = 3 x = -5CHALLENGE Find all values of k so that each trinomial can be factoredusing integers.44. x 2 + kx - 19 45. x 2 + kx + 1446. x 2 - 8x + k, k > 0 47. x 2 - 5x + k, k > 048. Writing in Math Use the information about Tamika’s garden on page 434to explain how factoring can be used to find the dimensions of a garden.Explain how your method is related to the process used to factor trinomialsof the form x 2 + bx + c.49. Which is a factor of x 2 + 9x + 18?A x + 2B x - 2C x + 3D x - 350. REVIEW An 8-foot by 5-foot sectionof wall is to be covered by square tilesthat measure 4 inches on each side.If the tiles are not cut, how manyof them will be needed to coverthe wall?F 30 H 360G 240 J 1440Solve each equation. Check the solutions. (Lesson 8-2)51. (x + 3)(2x - 5) = 0 52. 7b(b - 4) = 0 53. 5 y 2 = -9yFind the GCF of each set of monomials. (Lesson 8-1)54. 24, 72 55. 9p q5, 21 p 3 q 3 56. 30 x 2 , 75 x 3 y 4 , 20 x 4 z57. MUSIC Albertina practices the guitar 20 minutes each day. She wants to add5 minutes to her practice time each day until she is practicing at least 45minutes daily. How many days will it take her to reach her goal? (Lesson 6-3)PREREQUISITE SKILL Factor each polynomial. (Lesson 8-2)58. 3 y 2 + 2y + 9y + 6 59. 3 a 2 + 2a + 12a + 8 60. 4 x 2 + 3x + 8x + 661. 2 p 2 - 6p + 7p - 21 62. 3 b 2 + 7b - 12b - 28 63. 4 g 2 - 2g - 6g + 3Lesson 8-3 Factoring Trinomials: x 2 + bx + c 439

CHAPTER8Mid-**Chapter** QuizLessons 8-1 through 8-3Factor each monomial completely. (Lesson 8-1)1. 35mn 2. 27 r 23. 20 xy 3 4. 78 a 2 3b c5. THEATER Drama students have 140 chairs toplace in front of an outdoor stage. In whatways can they arrange the chairs so thatthere is the same number in each row, at least6 rows of chairs, and at least 6 chairs in eachrow? (Lesson 8-1)Find the GCF of each set of monomials.(Lesson 8-1)6. 24a b 2 , 21a 3 7. 18n, 25p 28. 15q 2 r 2 , 5r 2 s 9. 42x 2 y, 30xy 2Factor each polynomial. (Lesson 8-2)10. 3m + 18n11. 4xy 2 - xy12. 32a 2 b + 40b 3 - 8a 2 b 213. 6pq + 16p - 15q - 4014. PHOTOS Olinda is placing matting x incheswide around a photo that is 5 inches longand 3 inches wide. Write an expression infactored form for the area of thematting. (Lesson 8-2)440 **Chapter** 8 Factoring15. FOOTBALL In a football game, Darryl puntsthe ball downfield. The height h of thefootball above the ground after t seconds canbe modeled by h = 76.8t - 16t 2 . How longwas the football in the air? (Lesson 8-2)16. MULTIPLE CHOICE What are the rootsof d 2 - 12d = 0? (Lesson 8-2)A 0 and -12 C -12 and 12B 0 and 12 D 12 and 1217. GEOMETRY Write an expression in factoredform for the area of the shaded region.(Lesson 8-2) Solve each equation. Check the solutions.(Lesson 8-2)18. (8n + 5)(n - 4) = 019. 9x 2 - 27x = 020. 10x 2 = -3xFactor each trinomial. (Lesson 8-3)21. n 2 - 2n - 4822. x 2 - 4xy + 3y 223. a 2 + 5ab + 4b 224. s 2 - 13st + 36t 2Solve each equation. Check the solutions.(Lesson 8-3)25. a 2 + 7a + 10 = 026. n 2 + 4n - 21 = 027. x 2 - 2x - 6 = 7428. x 2 - x + 56 = 17x29. GEOMETRY The rectangle has an area of 180square feet. Find the width w of therectangle. (Lesson 8-3)30. MULTIPLE CHOICE Which represents one ofthe roots of 0 = x 2 + 3x - 18? (Lesson 8-3)F -6 H 6G -3J1_3

- 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
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- 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 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 42 and 43: Solve each equation. Check the solu
- 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