# College Algebra

Barron's Educational Series, 1995 - Mathematics - 218 pages
Books in the " EZ-101 Study Keys " series are intended as brush-up reviews for a variety of college-101 courses. They are designed as a set of classroom "notes" that reflect typical lecture material presented in a classroom over the course of a semester. As such, they make handy supplements to college textbooks and serve as valuable pre-exam reviews. Covered in this updated edition are polynomials, radicals, equations and inequalities, polynomial equations, exponential and logarithmic functions, conics, sequences and series, induction, permutations and combinations, determinants and matrices, and more.

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### Contents

 Basic laws and operations of algebra 1 Sets numbers and variables 2 Equality and inequality relations 4 Field properties of real numbers 5 Interval notation 7 Integer exponents 8 Polynomials 11 Factoring polynomials 15
 Synthetic division 113 The remainder and factor theorems 116 Zeros of polynomial functions 117 Reducing the degree of a polynomial equation 119 The rational root theorem 121 Descartes rule of signs 123 Locating and approximating irrational roots 125 Exponential and logarithmic functions 127

 Radicals and rational exponents 18 Operations with radicals 20 Equations and inequalities 23 Linear equations 24 Linear inequalities 28 Absolute value equations and inequalities 30 Quadratic equations 33 Quadratic inequalities 37 Radical equations 39 Rational expressions 42 Simplifying rational expressions 43 Operations with rational expressions 45 Simplifying complex fractions 49 Fractional equations and inequalities 50 Linear equations and inequalities in twovariables 53 Midpoint and distance formulas 54 Slope formula 58 Equations of lines 61 Graphing linear equations in two variables 64 Graphing linear inequalities in two variables 66 Complex numbers and quadratic equations 68 Complex numbers 69 Solving quadratic equations by completing the square 72 Solving quadratic equations by formula 73 Sum and product of the roots 75 Graphing quadratic equations in two variables 77 Functions and their graphs 82 Functions 83 Vertical and horizontal line tests 86 Symmetry and functions 88 Graphs of special functions 91 Shifts of graphs of functions 96 The composition of two functions 100 Inverse functions 102 Polynomial and rational functions 104 Graphing rational functions 106 Equations that describe variation 109 Polynomial equations 112
 Exponential functions 128 Logarithmic functions 131 Logarithm laws 134 Exponential and logarithmic equations 136 Exponential growth and decay 139 Conic sections and their equations 142 The circle 144 The ellipse 145 The hyperbola 149 The parabola 155 The general equation for conic sections 159 Counting methods 161 The basic principles of counting 162 Permutations 163 Combinations 165 The binomial theorem 167 Sequences series and induction 169 Arithmetic sequences and series 170 Geometric sequences and series 172 Generalized sequences 174 Summation notation 176 Mathematical induction part I 179 Mathematical induction part II 182 Linear and nonlinear systems 184 Solving systems of two linear equations 185 Matrices 187 Determinants 190 Cramers rule 193 Triangularizing linear systems 195 Recognizing linear systems that have many or no solutions 198 Finding the inverse of a matrix 199 Solving linear systems by matrix inversion 201 Partial fractions 203 Solving nonlinear systems 206 Glossary 209 Index 216 Copyright

### Popular passages

Page 212 - ... is less than is less than or equal to is greater than is greater than or equal to...
Page 210 - A complex number is any number that can be written in the form a + hi, where a and b are real numbers and / = V— T.
Page 213 - It is also clear that if A is an mxn matrix and B is an nxp matrix, then C is an mxp matrix.