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5-5 Solving Polynomial Equations Therefore, the solutions are Factor completely. If the polynomial is not factorable, write prime . 4 . 3 35. 64x + 1 = 0 SOLUTION: 3 21. 64x + xy SOLUTION: Solve each equation. 4 2 32. x – 7x – 44 = 0 SOLUTION: 2 Let y = x . Therefore, the solutions are . Factor completely. If the polynomial is not factorable, write prime. 6 50. x – 64 SOLUTION: Therefore, the solutions are . 3 35. 64x + 1 = 0 SOLUTION: 57. GEOMETRY The volume of the figure at the right is 440 cubic centimeters. Find the value of x and the length, height, and width. SOLUTION: The volume of the figure in terms of x is . eSolutions Manual - Powered by Cognero Therefore, the solutions are . Therefore, Solve for x. . Page 1 2 The expression x + 8x + 55 is a prime. Therefore, x = 8. The length is x= 8. The height is x + 3 = 11. The width is x – 3 = 5. 5-5 Solving Polynomial Equations 57. GEOMETRY The volume of the figure at the right is 440 cubic centimeters. Find the value of x and the length, height, and width. 70. ORGANIZE IDEAS A rectangular prism with dimensions x – 2, x – 4, and x – 6 has a volume equal to 40x cubic units. a. Write out a polynomial equation using the formula for volume. b. Use factoring to solve for x. c. Are any values for x unreasonable? Explain. d. What are the dimensions of the prism? SOLUTION: a. The volume of the prism is SOLUTION: The volume of the figure in terms of x is . Therefore, Solve for x. . Therefore, b. Solve for x. . By Zero Product Property: 2 The expression x + 8x + 55 is a prime. Therefore, x = 8. The length is x= 8. The height is x + 3 = 11. The width is x – 3 = 5. The solutions are 70. ORGANIZE IDEAS A rectangular prism with dimensions x – 2, x – 4, and x – 6 has a volume equal to 40x cubic units. a. Write out a polynomial equation using the formula for volume. b. Use factoring to solve for x. c. Are any values for x unreasonable? Explain. d. What are the dimensions of the prism? SOLUTION: a. The volume of the prism is and 12. c. Sample answer: ±2i because they are imaginary numbers. d. x – 2 =12 – 2 = 10 x – 4 = 12 – 4 = 8 x – 6 = 12 – 6 = 6 The dimensions are 6, 8 and 10 units. . Therefore, b. Solve for x. eSolutions Manual - Powered by Cognero Page 2