College Algebra Explained

Become a Master of College Algebra and Ace your next Algebra Exam! In this course, you will master all concepts of Algebra, from beginner to advanced, with our step-by-step video tutorials and test your knowledge with over 2500 Practice Test Questions. The concepts you will learn are fundamental to success in higher math classes such as Trigonometry and Calculus. The topics of the course include:

• Review of Real Numbers

• Operations with Polynomials

• Factoring Polynomials

• Rational Expressions

• Rational Exponents

• Radical Expressions

• Solving Linear Equations/Inequalities

• Solving Word Problems with Linear Equations

• Complex Numbers

• Solving Quadratic Equations (Factoring, Completing the Square, Quadratic Formula)

• Solving Word Problems with Quadratic Equations

• Solving Quadratic/Rational Inequalities

• Solving Radical Equations/Inequalities

• Solving Advanced Absolute Value Equations/Inequalities

• The Coordinate Plane

• Graphing Circles

• Distance and Midpoint Formulas

• Relations and Functions

• Domain and Range

• Vertical Line Test

• Increasing, Decreasing, Constant Intervals

• Graphing Linear Functions

• Slope

• Forms of a Line

• Graphs of Basic Equations (Parent Functions)

• Graphing Transformations

• Function Operations

• The Difference Quotient

• Composition of Functions

• Solving Linear Systems in Two/Three Variables

• Solving Systems of Linear Inequalities in Two Variables

• Solving Word Problems with Linear Systems

• Curve Fitting, Finding the Equation of a Parabola Given Three Points

• Partial Fraction Decomposition

• Solving Linear Systems using Gaussian Elimination and Gauss-Jordan Elimination

• Matrix Algebra (Adding Matrices, Multiplying Matrices, Solving Matrix Equations)

• Finding the Inverse of a Matrix

• Solving Linear Systems using the Inverse of a Matrix

• Finding the Determinant of a Matrix

• Finding the Inverse of a Matrix Using Cofactors

• Solving Linear Systems using Cramer's Rule

• Applications of determinants: Area of a Triangle, test for collinearity, equation of a line

• Determine if functions are one-to-one using the Horizontal line test/algebraic methods

• Finding the Inverse of a One-to-One Function

• Finding the Inverse of a Domain Restricted Function

• Graphing the Inverse of a Function

• Graphing Exponential Functions

• Solving Exponential Equations with Like Bases

• Solving Compound Interest Word Problems

• Solving Continuous Compound Interest Word Problems

• Graphing Logarithmic Functions

• Properties of Logarithms

• Expanding Logarithms

• Condensing Logarithms

• Change of Base Rule for Logarithms

• Solving Exponential and Logarithmic Equations

• Finding the Vertex Form of a Parabola

• How to Graph a Parabola

• The Remainder Theorem

• Using the Remainder Theorem to test for Zeros of a Polynomial Function

• The Factor Theorem

• Using the Factor Theorem to factor a polynomial function given one zero

• Using the Rational Zeros Theorem to find all possible rational zeros

• The Fundamental Theorem of Algebra and the Number of Zeros Theorem

• Writing Polynomial Functions Given Zeros and a Point

• Conjugate Zeros Theorem

• Descartes' Rule of Signs

• Intermediate Value Theorem

• Boundedness Theorem

• Find the upper and lower bounds for zeros of a polynomial function

• Solving nonlinear systems of equations

• Conic Sections: Parabolas - Focus and Directrix

• Conic Sections: Ellipses - Finding the Foci and Graphing

• Arithmetic Sequences

• Arithmetic Series

• Geometric Sequences

• Geometric Series

• The Binomial Theorem

• Counting Theory

• Combinations

• Permutations

• Probability