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1 A.2c (a) Factoring polynomials SOL Warm-Up 1. Which of the following represents 12x 2 + 6x + 3 in simplified form after factoring out the greatest common factor? A 12(x 2 + 2x + 4) B x(12x 2 + 6x + 3) C 3(4x 2 + 2x + 1) D 2(6x 2 + 3x + 1) 2. Which of the following represents 4x 3 + 8x x in factored form after factoring out the greatest common factor? A 4(x 3 + 2x 2 + 3x) B 2x(2x 2 + 4x + 6) C 4(x 3 + 8x x) D 4x(x 2 + 2x + 3) 3. Which of the following represents 9a 2 b a 3 b 2 in factored form after factoring out the greatest common factor? A 9a 2 b 2 (b 2 + 2a) B 3ab(3ab 2 + 6a 2 b) C 9a 3 b 4 (1 + 2ab) D 6a 2 b 2 (3b 2 + 3a) 4. Which of the following represents 2x 2-2x in factored form after factoring out the greatest common factor? A 2(x 2 - x) B x(2x - 2) C 2x(x - 1) D 2x 2 (1 - x)
2 A.2c (b) Factoring polynomials SOL Warm-Up 1. Which of the following expresses x 2 + 7x - 30 in simplified factored form? A (x - 3)(x + 10) B (x + 3)(x - 10) C (x - 6)(x + 5) D (x + 6)(x - 5) 2. Which of the following expresses x 2 + x - 12 in simplified factored form? A (x - 3)(x + 4) B (x + 3)(x - 4) C (x + 1)(x + 12) D (x + 6)(x + 2) 3. Which of the following expresses 2x 2 + 9x + 10 in simplified factored form? A (2x -2)(x + 5) B (2x - 5)(x - 2) C (2x + 1)(x + 10) D (2x + 5)(x + 2) 4. Which of the following expresses 2x 2-50 in simplified factored form? A 2(x - 1)(x + 5) B 2(x - 5)(x + 5) C (2x + 5)(x + 10) D (2x - 5)(x - 10)
3 A.2c (c) Factoring polynomials 1. Which of the following expresses x 2 + 7x + 12 in simplified factored form? A (x + 3)(x + 4) B (x - 3)(x - 4) C (x + 6)(x + 2) D (x + 5)(x + 2) 2. Which of the following expresses 4x 2 + 7x + 3 in simplified factored form? A (2x + 1)(2x + 3) B (4x + 3)(x + 1) C (4x + 1)(x + 3) D (x + 7)(x + 4) 3. Which of the following expresses x 2-64 in simplified factored form? A (x - 8)(x + 8) B (x + 4)(x - 16) C (x - 4)(x + 16) D (x + 64)(x - 1)
4 A.2c (d) Factoring polynomials 1. The area of a rectangle is calculated by multiplying the length by the width. If the area of a rectangle is x x + 10, which of the following could be the length of the rectangle? A x + 5 B x + 1 C x + 11 D x 5 2. The area of a rectangle is calculated by multiplying the length by the width. If the area of a rectangle is 3x 2-23x 36, which of the following could be the length of the rectangle? A 3x + 4 B 3x + 12 C x + 9 D 3x The area of a rectangle is calculated by multiplying the length by the width. If the area of a rectangle is 2x 2 + 7x + 6, which of the following could be the length of the rectangle? A x + 6 B x + 2 C x + 7 D 2x + 7
5 A.2c (e) Factoring polynomials 1. The area of a circle is r 2 and the area of a rectangle is LW. Which of the following could represent the area of the shaded region in the drawing? A 2r(r - ) B 4r(r - ) C 2r 2 ( - r) D r 2 (4 - ) 2. The area of a circle is πr 2 and the area of a rectangle is LW. Which of the following could represent the area of the shaded region in the drawing? A (r ) B r 2 (12 + ) C 6r( + 2) D 6r 2 (3 + 2 )
6 A.2c (f) Using x-intercepts to factor a polynomial 1. Which of the following represents the factored form of a polynomial with (-2, 0) and (-3, 0) as its x-intercepts? A (x + 2)(x + 3) B (x - 2)(x - 3) C (x + 2)(x - 3) D (x - 2)(x + 3) 2. Which of the following represents the factored form of a polynomial with ( 3, 0) and (-1, 0) as its x-intercepts? 2 A (x - 3 )(x - 1) 2 B (-x + 3 )(x + 1) 2 C (2x - 3)(x + 1) D (2x - 3)(x - 1) 3. Which of the following represents the factored form of a polynomial with (0, 0) and (-6, 0) as its x-intercepts? A x(x + 6) B (x - 6)(x + 6) C (x + 6)(x + 6) D x(x - 6)
7 A.2c (a) Solving quadratic equations SOL Warm-Up 1. What are the solutions of x 2 + 5x + 6 = 0? A x = -2 or x = -3 B x = 2 or x = 3 C x = -6 or x = 1 D x = -1 or x = 6 2. What are the solutions of x 2-15 = 2x? A x = 0 or x = -2 B x = -5 or x = 3 C x = 0 or x = 2 D x = -3 or x = 5 3. What are the solutions of x 2 = 7x? A x = 0 or x = -7 B x = 4 or x = 3 C x = 0 or x = 7 D x = 7 only 4. What are the solutions of 2x 2 = x + 3? A x = -3 or x = 2 B x = 3/2 or x = -1 C x = 3 or x = -2 D x = 3 or x = -1
8 A.4c (b) Solving quadratic equations 1. What are the solutions of x x + 30 = 0? A x = 2 or x = 15 B x = -5 or x = -6 C x = -15 or x = -2 D x = 6 or x = 5 2. What are the solutions of x 2-30 = 6? A x = 0 or x = -6 B x = 6 or x = -6 C x = 0 or x = 6 D x = -6 only 3. What are the solutions of x 2 + x - 20 = 0? A x = 5 or x = -4 B x = -5 or x = -4 C x = 5 or x = 4 D x = -5 or x = 4
9 A.4c (c) Solving quadratic equations 1. What are the dimensions of a rectangle if the length is 7 less than twice the width and the area is 30? A 5 by 6 B 15 by 2 C 4 by 7.5 D 3 by What are the dimensions of a rectangle if the length is 2 more than the width and the area is 48? A 12 by 4 B 3 by 16 C 6 by 8 D 5.5 by 7.5
10 A.4c (d) Solving quadratic equations 1. What are the dimensions of a rectangle if the length is 7 less than twice the width and the area is 72? A 12 by 6 B 18 by 4 C 10 by 7.2 D 9 by 8 2. What are the dimensions of a rectangle if the length is 5 less than three times the width and the area is 78? A 6 by 13 B 3 by 26 C 10 by 7.8 D 2 by 39
11 A.4c (e) Identifying x-intercepts of a quadratic function 1. What are the x-intercepts of the graph of 2x 2-5x - 3? A ( 3, 0) (-1, 0) 2 B ( 1 3, 0) ( 9 2, 0) C ( 1, 0) (3,0) 2 D ( 1, 0) (-9, 0) 6 2. What are the x-intercepts of the graph of 4x 2-4x + 1? A (-1, 0) ( 1 2, 0) B (-1, 0) (1, 0) C (1, 0) D ( 1 2, 0) 3. What are the x-intercepts of the graph of 9x 2-1? A ( 1 9, 0) ( 1 9, 0) B (1, 0) (-1, 0) C ( 1 3, 0) D ( 1 3, 0) (- 1 3, 0)
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![[1] [2.3 b,c] [2] [2.3b] 3. Solve for x: 3x 4 2x. [3] [2.7 c] [4] [2.7 d] 5. Solve for h : [5] [2.4 b] 6. Solve for k: 3 x = 4k](/thumbs/78/77023587.jpg "[1] [2.3 b,c] [2] [2.3b] 3. Solve for x: 3x 4 2x. [3] [2.7 c] [4] [2.7 d] 5. Solve for h : [5] [2.4 b] 6. Solve for k: 3 x = 4k")
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