# Algebra

Springer Science & Business Media, Jul 9, 2003 - Mathematics - 160 pages

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I am using this book as the guiding text for teaching a teen who missed much of his mathematical instruction prior to high school. It is ideal because the authors carefully build the necessary mathematical understandings from one problem to the next.
This text will be completed in two years with this boy. I decided to leave chapters 33 through 45 for his second year of algebra, skipping ahead as we approach the end of the first year (Algebra 1). We picked up with chapter 46 "Equations" with a plan to do as much as we can fit in before pausing this summer.
I have not skipped a single problem. I have been tempted, but every time I have been glad that I persevered. Every problem has something to teach.
I love the absence of distracting photographs, sidebars, and such. If I feel that something of nature will add to the instruction, I find my own and add it into the assignment. By the time I finish with this boy, I will have a wonderful set of assignments all recorded and ready to go for another student. There are being developed and stored on WPIs software, ASSISTments.

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### Contents

 1 Introduction 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 Copyright