24. Find, describe, and correct the error below in determining the sum of the expressions:

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1 SECONDARY 3 HONORS ~ Unit 2A Assignments SECTION 2.2 (page 69): Simplify each expression: Given the binomials and, how would you find the product? 13. Is the product of two polynomials and closed under multiplication? Explain. 14. The length of a rectangle is 12 feet longer than the width. Write an expression to show the area of a rectangle. (Think - what is the formula for the area of a rectangle? How can you express the length and width of the rectangle?) 15. Ryan planted flowers in a rectangular garden. The width of the garden is feet and the length of the garden is 2 feet longer than the width. Write an expression for the area of the garden. 16. The cost of running a company last year was, where is the number of widgets produced. The amount of revenue the company made last year was, where is the number of widgets produced. Write an expression for the profit the company made last year for producing widgets. 17. Is the difference of two polynomials and always a polynomial? Explain. Simplify each expression: Find, describe, and correct the error below in determining the sum of the expressions: 25. Edith has a rectangular picture frame. The length of the frame is inches, and the width of the frame is 5 inches shorter than the length. Write an expression for the perimeter of the picture frame.

2 SECTION 2.1 (page 61): Classify each polynomial by degree and by number of terms: Write each polynomial in standard form: Describe the end behavior of the graph of 14. Can the graph of a polynomial function be a straight line? If so, give an example. 15. Your friend claims the graph of the function has only one turning point. Describe the error your friend made and give the correct number of turning points. 16. The data in the table to the right shows the power generated by a wind turbine. The column gives the wind speed in meters per second. The column gives the power generated in kilowatts. What is the degree of the polynomial function that models the data? (Think of a plan: What are the first differences of the y-values? What are the second differences of the y-values? When are the differences constant?) X Y Classify each polynomial by degree and by number of terms. Simplify first if necessary Determine the sign of the leading coefficient and the least possible degree of the polynomial function for each graph Write an equation for a polynomial function that has 3 turning points and end behavior up and up. LAB Exercises (page 65): Determine whether each function is even, odd, or neither

3 SECONDARY 3 HONORS ~ Unit 2A Assignments SECTION 2.3 (page 78): Find the zeros of each function Write a polynomial function in standard form with zeros -1, 1, and Write a polynomial function in standard form that has 3 and -5 as zeros of multiplicity Your friend says that to write a function that has zeros 3 and -1, you should multiply the two factors (x+3) and (x-1) to get. Describe and correct your friend s error. Write each function in factored form. Check by multiplication A storage company needs to design a new storage box that has twice the volume of its largest box. Its largest box is 5 ft. long, 4 ft. wide, and 3 ft. high. The new box must be formed by increasing each dimension by the same amount. Find the increase in each dimension. (Think: How can you write the dimensions of the new storage box as polynomial expressions? How can you use the volume of the current largest box to find the volume of the new box?) 22. A carpenter hollowed out the interior of a block of wood as shown at the right. a) Express the volume of the original block and the volume of the wood removed as polynomials in factored form. b) What polynomial represents the volume of the wood remaining? 23. A rectangular box is 2x+3 units long, 2x-3 units wide, and 3x units high. What is its volume, expressed as a polynomial? 24. The volume in cubic feet of a CD holder can be expressed as or, when factored, as the product of its three dimensions. The depth is expressed as. Assume that the height is greater than the width. a) Factor the polynomial to find linear expressions for the height and width. b) Graph the function. Find the x-intercepts. What do they represent? c) What is a realistic domain for the function? d) What is the maximum volume of the CD holder? Find the relative maximum, relative minimum, and zeros of each function Write a polynomial function with the following features: it has three distinct zeros; one of the zeros is 1; another zero has a multiplicity of 2.

4 (Section 2.3, continued) 29. Explain how the graph of a polynomial function can help you factor the polynomial. For each function, determine the zeros. State the multiplicity of any multiple zeros Find a fourth-degree polynomial function with zeros 1, -1, i, and -i. Write the function in factored form. SECTION 2.4 (page 86) Factor each polynomial: Solve each equation by factoring: Identify each of the following as a sum of cubes, a difference of cubes, or a difference of squares: a) b) c) d) 16. Which method of solving polynomial equations will not identify the imaginary roots? Explain. 17. Show two different ways to find the real roots of the polynomial equation. Show your steps. Solve each equation The width of a plastic storage box is 1 ft. longer than the height. The length is 4 ft longer than the height. The volume is 36 ft 3. What are the dimensions of the box? (Think: What is the formula for the volume of a rectangular prism? What variable equations represent the length, height, and width? What equation represents the volume of the plastic storage box?) 31. A student claims that 1, 2, 3, and 4 are the zeros of a cubic polynomial function. Explain why the student is mistaken. 32. The width of a box is 2 m less than the length. The height is 1 m less than the length. The volume is 60 m 3. What is the length of the box? Graph each function to find the zeros. Rewrite the function with the polynomial in factored form

5 SECONDARY 3 HONORS ~ Unit 2A Assignments SECTION 2.5 (page 95): Use synthetic division and the remainder theorem to find Divide using any method A polynomial is divided by a binomial, the remainder is zero. What conclusion can you draw? Explain. 17. Explain why it is important to have the terms of both polynomials written in descending order of degree before dividing. 19. Your friend multiplies by a quadratic polynomial and gets the result. The teacher says that everything is correct except for the constant term. Find the quadratic polynomial that your friend used. What is the correct result of the multiplication? (Think: What does the fact that all terms except for the constant are correct tell you? How can polynomial division help you solve this problem? What is the connection between the remainder of the division and you friend s error?) 20. A student used synthetic division to divide by. Describe and correct the error shown When a polynomial is divided by, the quotient is with remainder 7. Find the polynomial. 22. The expression represents the volume of a square pyramid. The expression Divide: represents the height of the pyramid. What expression represents the side length of the base? (Hint: The formula for the volume of a pyramid is.)

6 (Section 2.5 continued) Determine whether each binomial is a factor of Divide using synthetic division Divide. Look for patterns in your answers. a) b) c) d) Using the patterns, factor 44. Use synthetic division to find