3. Write a polynomial function, p(x), with degree 3 that has p(7) = 0. Lesson 15 Practice Problems 1. For the polynomial function f(x) = x3 - 2x2 - 5x + 6, we have f(0) = 6, f(2) = -4. f(-2) = 0, f(3) = 0, f(-1) = 8, f(1) = 0. Rewrite f(x) as a product of linear factors . 4. Long division was n was used here to divide the polynomial function p(x) = x3+7x2 - 20x - 110 by (x - 5) and to divide it by (x + 5). *2 + 12x +40 x - 5) x3+7x2 -20x- 110 x2 + 2x - 30 -x3 + 5x2 x+5)x3+7x2- 20x-110 12x2 - 20x -x3 - 5x2 -12x2 + 60x 2x2 - 20x 40x - 110 -2x2 - 10x -30x - 110 -40x + 200 30x + 150 a. What is p(-5)? 2. Select all the polynomials that have (x - 4) as a factor. b. What is p(5)? A. x3 - 13x - 12 5. Which polynomial function has zeros when x = 5, 3,-7? B. x3 + 8x2 + 19x + 12 A. f(x) = (x+5)(2x+3)(x-7) C. x3 + 6x +5x - 12 D. X3 - x2 - 10x - 8 B. f(x) = (x+5)(3x+2)(x-7) E. x2 - 4 C. f (x) = (x-5)(2x-3)(x+7) D. f(x) = (x-5)(3x-2)(x+7) (From Unit 2, Lesson 5.)return shift Lesson 16 Practice Problems or odd? Explain your reasoning. The graph of a polynomial function f is shown. Is the degree of the polynomial event 1. There are many cylinders with a volume of 144x cubic inches. The height h(r) in inches of one of these cylinders is a function of its radius r in inches where "(P) = 144 a. What is the height of one of these cylinders if its radius is 2 inches? b. What is the height of one of these cylinders if its radius is 3 inches? C. What is the height of one of these cylinders if its radius is 6 inches? 2. The surface area S(r) in square units of a cylinder with a volume of 18 cubic units is a ( From Unit 2, Lesson 8.) -18 function of its radius r in units where S(r) = 2ar + . What is the surface area of a cylinder with a volume of 18 cubic units and a radius of 3 units? 5. The polynomial function p(x) = x* + 4x3 - 7x3 - 22x + 24 has known factors of (x + 4) and (x - 1). a. Rewrite p(x) as the product of linear factors. 3. Han finds an expression for S(r) that gives the surface area in square inches of any cylindrical can with a specific fixed volume, in terms of its radius r in inches. This is the graph Han gets if he allows r to take on any value between -1 and 5. b. Draw a rough sketch of the graph of the function. a. What would be a more appropriate domain for Han to use instead? b. What is the approximate minimum surface area for the can? 2 (From Unit 2, Lesson 12.)