Lesson 2 Practice Problems 1. Select all polynomial expressions that are equivalent to 6x4 + 4x3 __ 7x2 + 5x + 8. A. 16xlo B. 6x5 +4x4 7x3 + 5x2 + 8x C. 6):4 +4):3 7x2 +5x+ g D. 8+5x+7x2 4x3 +6x4 E. 8+5x7x2 +4x3 +6x4 2. Each year a certain amount of money is deposited in an account which pays an annualinterest rate of r so that at the end of each year the balance in the account is multiplied by a growth factor of x = 1 + r. $500 is deposited at the start of the first year, an additional $200 is deposited at the start of the next year, and $600 at the start 0f the following year. a. Write an expression for the value of the account at the end of three years in terms of the growth factor x. b. What is the amount (to the nearest cent) in the account at the end of three years if the interest rate is 2%? 3. Consider the polynomial function p given by p(x) = 5x3 + 8x2 3x + 1. Evaluate the function at x = -2. 85 .2 Lesson 2 Practice Problems 4. An open-top box is formed by cutting squares out of a 5 inch by 7 inch piece of po and then folding up the sides. The volume V(x) in cubic inches of this type of Paper open-top box is a function of the side length x in inches of the square cutouts and can be given by V(x) = (7-2x)(5 -2x)(x). Rewrite this equation by expan 6. Tyler finds an expression for V(x) that panding the gives the volume of an open-top box in polynomial. cubic inches in terms of the length x in inches of the square cutouts used to make it. This is the graph Tyler gets if he allows x to take on any value between -1 and 7. 5. A rectangular playground space is to be fenced in using the wall of a daycare building for one side and 200 meters of fencing for the other three sides. The area A(x) in square meters of the playground space is a function of the length x in meters of each of the sides perpendicular to the wall of the daycare building. a. What is the area of the playground when x = 50? a. What would be a more appropriate domain for Tyler to use instead? b. Write an expression for A(x). b. What is the approximate maximum volume for his box? (From Unit 2, Lesson 1.) c. What is a reasonable domain for A in this context? (From Unit 2, Lesson 1.) CO iN VH Unit 2 Lesson 2 Practice ProblemsV Lesson 3 Practice Problems 1. Select all points where relatlve minimum values occur on this graph of a polynomial function. A. Point A B. Point B C. Point C D. Point D E. Point E F. Point F G. Point G l H. Point H .. 2. Add one term to the polynomial expression 14x19 9x15 + 111:4 + 5x2 + 3 to make it into 3 22nd degree polynomial. Unit 2 Lesson 3 Practice Problems 91 3. Identify the degree, leading coefficient, and constant value of each of the following polynomials: a. f ( x) = x3 - 8x2 - x+8 6. An open-top box is formed by cutting squares out of an 11 inch by 17 inch piece of paper and then folding up the sides. The volume V(x) in cubic inches of this type of open-top box is a function of the side length x in inches of the square cutouts and can be given by V(x) = (17 - 2x)(11 - 2x)(x). Rewrite this equation by expanding b . h (x ) = 2x4 + x3 - 3x2 - x+1 the polynomial. (From Unit 2, Lesson 2.) c. 8(x) = 13.2x3 + 3x4 - x -4.4 4. We want to make an open-top box by cutting out corners of a square piece of cardboard and folding up the sides. The cardboard is a 9 inch by 9 inch square. The volume V(x) in cubic inches of the open-top box is a function of the side length x in inches of the square cutouts. a. Write an expression for V(x). b. What is the volume of the box when x = 1? c. What is a reasonable domain for V in this context? (From Unit 2, Lesson 1.) 5. Consider the polynomial function p given by p(x) = 7x3 - 2x2 + 3x + 10. Evaluate the function at x = -3. (From Unit 2, Lesson 2.)