Vocabulary. Term Page Definition Clarifying Example. binomial. cubic. degree of a monomial. degree of a polynomial

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1 CHAPTER 7 Vocabulary This table contains important vocabulary terms from Chapter 7. As you work through the chapter, fill in the page number, definition, and a clarifying example for each term. binomial Term Page Definition Clarifying Example cubic degree of a monomial degree of a polynomial difference of two squares leading coefficient monomial perfect-square trinomial polynomial quadratic scientific notation 106 Algebra 1

2 CHAPTER 7 VOCABULARY CONTINUED Term Page Definition Clarifying Example standard form of a polynomial trinomial 107 Algebra 1

3 CHAPTER 7 Big Ideas Answer these questions to summarize the important concepts from Chapter 7 in your own words. 1. Explain why the properties using zero exponents and negative exponents specify that bases must be nonzero numbers. 2. Explain the difference between multiplying by powers of 10 when the exponent is a positive number and when the exponent is a negative number. 3. When is an exponential expression completely simplified? 4. Explain how to multiply (x 3)(x 2) using the FOIL method. For more review of Chapter 7: Complete the Chapter 7 Study Guide and Review on pages Compete the Ready to Go On quizzes on pages 475 and Algebra 1

4 CHAPTER 8 Chapter Review 8-1 Factors and Greatest Common Factors Write the prime factorization of each number Find the GCF of each pair of monomials r 4 and 12r z 3 and 32z x 2 y and 84xy s 6 t 3 and 45s 3 t Factoring by GCF Factor each polynomial. Check your answer. 9. 2s a 3 4a y 4 24y x 2 8x b 3 15b 2 33b p 3 21p 2 q Factor each polynomial by grouping. Check your answer. 15. r 3 3r 2 2r y 3 14y 2 y x 3 10x 2 3x Factoring x 2 bx c Factor each trinomial. Check your answer. 18. a 2 5a x 2 7x n 2 4n Algebra 1

5 CHAPTER 8 REVIEW CONTINUED 21. f 2 11f z 2 z t 2 t Factor x 2 7x 12. Check your answer. 8-4 Factoring ax 2 bx c Factor each trinomial. Check your answer a 2 5a s 2 17s y 2 18y z 2 12z x 2 44x t 2 31t The area of a rectangle is 5x 2 22x 8 cm 2. The width is (x 4) cm. What is the length of the rectangle? 8-5 Factoring Special Products Determine whether each trinomial is a perfect square. If so, factor it t 2 30t z 2 8z y 2 36y x 2 28x b 2 16b m 2 12m Algebra 1

6 CHAPTER 8 REVIEW CONTINUED Determine whether each trinomial is the difference of two squares. If so, factor it s t x h z y 4 16x Choosing a Factoring Method Factor each polynomial completely. Check your answer b 3 30b 2 60b 45. 2x 2 y 16xy 30y 46. c 3 6c 2 4c 24 Write an expression for the situation. Factor your expression. 47. Nine times the square of Teresa s shoe size plus twelve times Teresa s shoe size plus four 48. The difference of the square of four times a DVD cost and Algebra 1

7 CHAPTER 8 Big Ideas Answer these questions to summarize the important concepts from Chapter 8 in your own words. 1. Explain how to find the GCF of two terms that contain the same variable raised to different exponents. 2. What are the steps for factoring the GCF? 3. Explain, in words, how to factor the quadratic trinomial x 2 bx c. 4. Explain how to determine the signs of the factors of c when factoring a trinomial of the form x 2 bx c. For more review of Chapter 8: Complete the Chapter 8 Study Guide and Review on pages of your textbook. Compete the Ready to Go On quizzes on pages 557 and 573 of your textbook. 135 Algebra 1

8 Name: Class: Date: ID: B Algebra Quater 4 Exam Review Part 1 Short Answer 51. Tell whether the graph of the quadratic function y = 4x 2 4x + 4 opens upward or downward. Explain. 52. Identify the vertex of the parabola. Then give the minimum or maximum value of the function. 53. Find the domain and range. 1

9 Name: ID: B 54. Find the zeros of the quadratic function f x = 2x 2 6x 8 from the graph. 55. Find the axis of symmetry of the parabola. 56. Find the axis of symmetry of the graph of y = x 2 + 2x Find the axis of symmetry of the graph of y = x 2 + 2x Find the number of solutions of the equation 5x 2 + 5x + 3 = 0 by using the discriminant. 59. Find the number of solutions of the equation 8x 2 + 8x + 5 = 0 by using the discriminant. 2

10 Name: ID: B 60. Identify the sample space and the outcome shown for spinning the game spinner. 61. An experiment consists of spinning a spinner. Use the results in the table to find the experimental probability that the spinner does not land on green. Express your answer as a fraction in simplest form. Outcome Frequency red 9 purple 5 green A manufacturer inspects 500 personal video players and finds that 498 of them have no defects. The manufacturer sent a shipment of 1000 video players to a distributor. Predict the number of players in the shipment that are likely to have no defects. 63. The probability of drawing a green marble from a marble bag is 40%. What are the odds in favor of drawing a green marble? 64. Solve the equation a = 4. Check your answer. 65. Solve the equation 3 x = 15. Check your answer. 66. Find the excluded values of the rational expression 9 y y

11 -1- Algebra 1 Name ID: 2 Q4 Exam Review Part 2 Solve each equation by factoring. Date Period 67) (k 3)(2k 1) = 0 68) (n 2)(n + 1) = 0 69) (x + 3)(5x 3) = 0 70) (5x 1)(x + 5) = 0 71) (n 4)(n + 1) = 0 72) n 2 25 = 0 73) m 2 7m + 10 = 0 74) x 2 + x 6 = 0 75) p p 3 = 0 Solve each equation by taking square roots. 76) a 2 = 36 77) n 2 = 1 78) 36p 2 = 49 79) n = 30 80) b 2 4 = 12 81) x = 32 Solve each equation with the quadratic formula. 82) 5x 2 + 2x 24 = 0 83) 3k 2 4k 4 = 0 84) 6v 2 + 7v 68 = 0 Simplify.

12 -2-85) 12 86) 50 87) 18 88) 16n 2 89) 32x 2 90) ) ) ) ) ) ) Simplify each expression. 97) n2 16 n 4 98) x 5 5x 2 25x Simplify. 99) ( 3 + 3) 2 100) ( 3 + 5) 2