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1 Warm-Up Graphing Calculator Active Factoring polynomials 1. A B C D 2. A B C D 3. A B C D Which of the following represents 12x2 + 6x + 3 in simplified form after factoring out the greatest common factor? 12(x2 + 2x + 4) x(12x2 + 6x + 3) 3(4x2 + 2x + 1) 2(6x2 + 3x + 1) Which of the following represents 4x3 + 8x2 + 12x in factored form after factoring out the greatest common factor? 4(x3 + 2x2 + 3x) 2x(2x2 + 4x + 6) 4(x3 + 8x2 + 12x) 4x(x2 + 2x + 3) Which of the following represents 9a2b4 + 18a3b2 in factored form after factoring out the greatest common factor? 9a2b2(b2 + 2a) 3ab(3ab2 + 6a2b) 9a3b4(1 + 2ab) 6a2b2(3b2 + 3a) 4. Which of the following represents 2x2 - 2x in factored form after factoring out the greatest common factor? A B C D 2(x2 - x) x(2x - 2) 2x(x - 1) 2x2(1 - x) 2 Warm-Up Graphing Calculator Active Factoring polynomials 1. A B C D 2. A B C D 3. A B C D 4. A B C D Which of the following expresses x2 + 7x - 30 in simplified factored form? (x - 3)(x + 10) (x + 3)(x - 10) (x - 6)(x + 5) (x + 6)(x - 5) Which of the following expresses x2 + x - 12 in simplified factored form? (x - 3)(x + 4) (x + 3)(x - 4) (x + 1)(x + 12) (x + 6)(x + 2) Which of the following expresses 2x2 + 9x + 10 in simplified factored form? (2x -2)(x + 5) (2x - 5)(x - 2) (2x + 1)(x + 10) (2x + 5)(x + 2) Which of the following expresses 2x2 - 50 in simplified factored form? 2(x - 1)(x + 5) 2(x - 5)(x + 5) (2x + 5)(x + 10) (2x - 5)(x - 10) 3 4 Warm-Up Graphing Calculator Active Factoring polynomials 1. A B C D 2. A B C D 3. A B C D Which of the following expresses x2 + 7x + 12 in simplified factored form? (x + 3)(x + 4) (x - 3)(x - 4) (x + 6)(x + 2) (x + 5)(x + 2) Which of the following expresses 4x2 + 7x + 3 in simplified factored form? (2x + 1)(2x + 3) (4x + 3)(x + 1) (4x + 1)(x + 3) (x + 7)(x + 4) Which of the following expresses x2 - 64 in simplified factored form? (x - 8)(x + 8) (x + 4)(x - 16) (x - 4)(x + 16) (x + 64)(x - 1) 5 Warm-Up Graphing Calculator Active Factoring polynomials 1. A B C D 2. A B C D 3. A B C D The area of a rectangle is calculated by multiplying the length by the width. If the area of a rectangle is x2 + 11x + 10, which of the following could be the length of the rectangle? x+5 x+1 x + 11 x–5 The area of a rectangle is calculated by multiplying the length by the width. If the area of a rectangle is 3x2 - 23x – 36, which of the following could be the length of the rectangle? 3x + 4 3x + 12 x+9 3x – 23 The area of a rectangle is calculated by multiplying the length by the width. If the area of a rectangle is 2x2 + 7x + 6, which of the following could be the length of the rectangle? x+6 x+2 x+7 2x + 7 6 7 Warm-Up Graphing Calculator Active Factoring polynomials 1. A B C D 2. A B C D The area of a circle is r2 and the area of a rectangle is LW. Which of the following could represent the area of the shaded region in the drawing? 2r(r - ) 4r(r - ) 2r2( - r) r2(4 - ) The area of a circle is πr2 and the area of a rectangle is LW. Which of the following could represent the area of the shaded region in the drawing? (r2+ 12) r2(12 + ) 6r( + 2) 6r2(3 + 2 ) 8 Warm-Up Graphing Calculator Active Using x-intercepts to factor a polynomial 1. A B C D 2. Which of the following represents the factored form of a polynomial with (-2, 0) and (-3, 0) as its x-intercepts? (x + 2)(x + 3) (x - 2)(x - 3) (x + 2)(x - 3) (x - 2)(x + 3) Which of the following represents the factored form of a polynomial 3 with ( , 0) and (-1, 0) as its x-intercepts? 2 3 2 3 B (-x + )(x + 1) 2 A (x - )(x - 1) C (2x - 3)(x + 1) D (2x - 3)(x - 1) 3. A B C D Which of the following represents the factored form of a polynomial with (0, 0) and (-6, 0) as its x-intercepts? x(x + 6) (x - 6)(x + 6) (x + 6)(x + 6) x(x - 6) 9 Warm-Up Graphing Calculator Active Solving quadratic equations 1. A B C D 2. A B C D 3. A B C D 4. A B C D What are the solutions of x2 + 5x + 6 = 0? x = -2 or x = -3 x = 2 or x = 3 x = -6 or x = 1 x = -1 or x = 6 What are the solutions of x2 - 15 = 2x? x = 0 or x = -2 x = -5 or x = 3 x = 0 or x = 2 x = -3 or x = 5 What are the solutions of x2 = 7x? x = 0 or x = -7 x = 4 or x = 3 x = 0 or x = 7 x = 7 only What are the solutions of 2x2 = x + 3? x = -3 or x = 2 x = 3/2 or x = -1 x = 3 or x = -2 x = 3 or x = -1 10 11 Warm-Up Graphing Calculator Active Solving quadratic equations 1. A B C D 2. A B C D 3. A B C D What are the solutions of x2 + 11x + 30 = 0? x = 2 or x = 15 x = -5 or x = -6 x = -15 or x = -2 x = 6 or x = 5 What are the solutions of x2 - 30 = 6? x = 0 or x = -6 x = 6 or x = -6 x = 0 or x = 6 x = -6 only What are the solutions of x2 + x - 20 = 0? x = 5 or x = -4 x = -5 or x = -4 x = 5 or x = 4 x = -5 or x = 4 12 Warm-Up Graphing Calculator Active Solving quadratic equations 1. A B C D 2. A B C D What are the dimensions of a rectangle if the length is 7 less than twice the width and the area is 30? 5 by 6 15 by 2 4 by 7.5 3 by 10 What are the dimensions of a rectangle if the length is 2 more than the width and the area is 48? 12 by 4 3 by 16 6 by 8 5.5 by 7.5 13 Warm-Up Graphing Calculator Active Solving quadratic equations 1. A B C D 2. A B C D What are the dimensions of a rectangle if the length is 7 less than twice the width and the area is 72? 12 by 6 18 by 4 10 by 7.2 9 by 8 What are the dimensions of a rectangle if the length is 5 less than three times the width and the area is 78? 6 by 13 3 by 26 10 by 7.8 2 by 39 14 Warm-Up Graphing Calculator Active Identifying x-intercepts of a quadratic function What are the x-intercepts of the graph of 2x2 - 5x - 3? 1. 3 2 A ( , 0) (-1, 0) 1 9 3 2 1 ( , 0) (3,0) 2 1 ( , 0) (-9, 0) 6 B ( , 0) ( , 0) C D What are the x-intercepts of the graph of 4x2 - 4x + 1? 2. 1 2 A (-1, 0) ( , 0) B (-1, 0) (1, 0) C (1, 0) 1 D ( , 0) 2 3. What are the x-intercepts of the graph of 9x2 - 1? 1 9 1 9 A ( , 0) ( , 0) B (1, 0) (-1, 0) 1 C ( , 0) 3 1 1 D ( , 0) (- , 0) 3 3