## Algebra (Google eBook)This text has been adopted at: Holyoke Community College, Holyoke, MA University of Illinois in Chicago, Chicago, IL University of Chicago, Chicago, IL California State University, Hayward, CA Georgia Southwestern College, Americus, GA Carey Col |

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### Contents

1 | |

4 Addition in the decimal number system | 2 |

5 The multiplication table and the multiplication algorithm | 5 |

6 The division algorithm | 6 |

7 The binary system | 8 |

8 The commutative law | 11 |

10 The use of parentheses | 13 |

11 The distributive law | 14 |

38 Values of polynomials and interpolation | 72 |

39 Arithmetic progressions | 77 |

40 The sum of an arithmetic progression | 79 |

41 Geometric progressions 41 Geometric progressions | 81 |

42 The sum of a geometric progression | 83 |

43 Different problems about progressions | 85 |

44 The welltempered clavier | 87 |

45 The sum of an infinite geometric progression | 91 |

12 Letters in algebra | 15 |

13 The addition of negative numbers | 17 |

14 The multiplication of negative numbers | 18 |

15 Dealing with fractions | 21 |

16 Powers | 25 |

17 Big numbers around us | 26 |

18 Negative powers | 27 |

19 Small numbers around us | 29 |

20 How to multiply am by an or why our definition is convenient | 30 |

21 The rule of multiplication for powers | 32 |

The square of a sum | 33 |

23 How to explain the square of the sum formula to your younger brother or sister | 34 |

24 The difference of squares | 36 |

25 The cube of the sum formula | 39 |

26 The formula for a + 64 | 40 |

27 Formulas for a + 65 a + 66 and Pascals triangle | 42 |

28 Polynomials | 44 |

When are polynomials equal? | 46 |

30 How many monomials do we get? | 48 |

31 Coefficients and values | 49 |

32 Factoring | 51 |

33 Rational expressions | 56 |

35 Polynomial and rational fractions in one variable | 61 |

36 Division of polynomials in one variable the remainder | 62 |

37 The remainder when dividing by x a | 68 |

46 Equations | 94 |

47 A short glossary | 95 |

49 The case p 0 Square roots | 96 |

50 Rules for square roots | 99 |

51 The equation x2 + px + q 0 Problem 235 Solve the equation | 100 |

52 Vietas theorem | 102 |

53 Factoring ax2 f bx + c | 106 |

54 A formula for ax2 + bx + c 0 where a 0 | 107 |

55 One more formula concerning quadratic equations | 108 |

57 The graph of the quadratic polynomial | 110 |

58 Quadratic inequalities | 114 |

60 Biquadratic equations | 116 |

61 Symmetric equations | 117 |

62 How to confuse students on an exam | 118 |

63 Roots | 120 |

64 Noninteger powers | 123 |

65 Proving inequalities | 127 |

66 Arithmetic and geometric means | 130 |

67 The geometric mean does not exceed the arithmetic mean | 132 |

69 Geometric illustrations | 134 |

70 The arithmetic and geometric means of several numbers | 136 |

71 The quadratic mean | 144 |

72 The harmonic mean | 147 |

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### References from web pages

JSTOR: Algebra

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