A30 APPENDIX Review Skill Building In Problems 15–24, tell whether the expression is a monomial. If it is, name the variable and the coefficient and give the degree of the monomial. If it is not a monomial, state why not. 15. x2 3 16. − x4 2 17. x 8 18. − −x2 3 19. − + x x 2 5 3 2 20. − x x 6 8 5 2 21. − x x 8 1 2 22. − + x x 2 1 2 3 23. + − x x2 5 2 24. + x3 4 2 In Problems 25–34, tell whether the expression is a polynomial. If it is, give its degree. If it is not, state why not. 25. − x3 5 2 26. − x 1 4 27. 5 28. π− 29. − x x 3 5 2 30. + x 3 2 31. − y2 2 3 32. + z z 10 2 33. + − x x 5 1 2 3 34. + − + + x x x x 3 2 1 1 3 2 In Problems 35–60, add, subtract, or multiply, as indicated. Express your answer as a single polynomial in standard form. 35. ( ) ( ) + + + − x x x 4 5 3 3 2 36. ( ) ( ) + + + − + x x x x 3 2 4 4 3 2 2 37. ( ) ( ) − + + − − + x x x x x 2 5 10 2 4 3 3 2 2 38. ( ) ( ) − − − − + + x x x x x 3 4 3 5 2 3 2 39. ( ) ( ) + − − − x x x x 6 3 4 2 3 3 2 3 2 40. ( ) ( ) − − − + − x x x x 8 4 3 1 6 4 8 2 3 2 3 41. ( ) ( ) − + − − y y y 9 3 4 6 1 2 2 42. ( ) ( ) − + + + + y y y y 8 1 4 1 3 2 3 43. ( ) + − x x x 4 2 44. ( ) − + x x x 4 2 2 3 45. ( )( ) + + x x 2 4 46. ( )( ) + + x x 3 5 47. ( )( ) + + x x 2 5 2 48. ( )( ) + + x x 3 1 2 1 49. ( )( ) − + x x 7 7 50. ( )( ) − + x x 1 1 51. ( )( ) + − x x 2 3 2 3 52. ( )( ) + − x x 3 2 3 2 53. ( ) +x 4 2 54. ( ) −x 5 2 55. ( ) −x2 3 2 56. ( ) −x3 4 2 57. ( ) −x 2 3 58. ( ) +x 1 3 59. ( ) +x2 1 3 60. ( ) −x3 2 3 In Problems 61–76, find the quotient and the remainder. Check your work by verifying that ⋅ + = Quotient Divisor Remainder Dividend 61. − + + x x x 4 3 1 3 2 divided by +x 2 62. − + − x x x 3 2 3 2 divided by +x 2 63. − + + x x x 4 3 1 3 2 divided by x2 64. − + − x x x 3 2 3 2 divided by x2 65. − + + x x x 5 3 1 4 2 divided by + x 2 2 66. − + − x x x 5 2 4 2 divided by + x 2 2 67. − + + x x x 4 3 1 5 2 divided by − x2 1 3 68. − + − x x x 3 2 5 2 divided by − x3 1 3 A.3 Assess Your Understanding Concepts and Vocabulary 1. The polynomial − + − x x x 3 2 13 5 4 3 2 is of degree . The leading coefficient is . 2. x x 4 4 2 2 ( )( ) − + = . 3. x x x 2 2 4 2 ( ) ( ) − + + = . 4. True or False −x4 2 is a monomial of degree −2. 5. True or False ( ) ( ) + + + = + x a x ax a x a . 2 3 3 6. True or False The polynomial + x 4 2 is prime. 7. True or False ( ) ( ) − − + = − + x x x x x 3 2 6 4 3 2 2 . 3 2 2 8. To complete the square of the expression + x x5 , 2 you would the number . 9. To check division, the expression that is being divided, the dividend, should equal the product of the and the plus the . 10. Multiple Choice The monomials that make up a polynomial are called which of the following? (a) terms (b) variables (c) factors (d) coefficients 11. Multiple Choice Choose the degree of the monomial x3 4 . (a) 3 (b) 7 (c) 4 (d) 2 12. Multiple Choice Choose the best description of − x 64 2 . (a) Prime (b) Difference of two squares (c) Difference of two cubes (d) Perfect Square 13. Multiple Choice Choose the complete factorization of − − x x 4 8 60 2 (a) ( )( ) + − x x 2 3 5 (b) ( ) − − x x 4 2 15 2 (c) ( )( ) + − x x 2 6 2 10 (d) ( )( ) + − x x 4 3 5 14. Multiple Choice To complete the square of + x bx 2 , use which of the following? (a) ( )b2 2 (b) b2 2 (c) ( )b 1 2 2 (d) b 1 2 2 1. Now Work 1. Modeling 1.ExplainingConcepts Calculus Preview 1.InteractiveFigure
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