## College AlgebraBooks 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 |

209 | |

216 | |

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### Common terms and phrases

algebra axis of symmetry binomial called complex numbers conjugate constant contains coordinate corresponding Cramer's rule degree denominator denoted determinant directrix divisor domain element ellipse endpoints equa equal equation P(x equation x2 exponential function exponents Figure foci functions OVERVIEW geometric sequence gives graph of f(x Hence horizontal line test hyperbola imaginary numbers INDIVIDUAL KEYS integer intersect inverse functions KEY EXAMPLE Solve linear equations linear system logarithm Mathematical induction matrix midpoint monomial multiplying each term negative notation number line numbers greater numerical coefficients obtained one-to-one function ordered pairs original equation parabola partial fraction permutations polynomial equation polynomial function positive integer quadratic equation quotient radical rational expressions rational root theorem rational roots real numbers real roots replace represents set of real side simplify slope standard form subtracting theorem tion variable variations in sign vertex vertical Write x-axis y-axis y-intercept zero

### 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.