# College Algebra Explained

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- 50 hours on-demand video
- 147 articles
- 147 downloadable resources
- Full lifetime access
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Try Udemy for Business- Review of Basic Concepts: Real Numbers, Order of Operations, Number Line, Absolute Value
- Review of Polynomials: Adding, Subtracting, Multiplying, Dividing, Synthetic Division, Factoring
- Review of Rational Expressions: Lowest Terms, Undefined, Addition, Subtraction, Multiplication, Division, Complex Fractions
- Review of Radical Expressions: Radical Notation, Simplifying a Radical, Operations with Radicals, Rationalizing Denominators
- Solving Linear Equations and Inequalities
- Solving Application of Linear Equations Problems (Word Problems)
- Solving Absolute Value Equations and Inequalities
- Working with Complex Numbers
- Solving Quadratic Equations and Inequalities
- Solving Applications of Quadratic Equations (Word Problems)
- Solving Rational Equations and Inequalities
- Solving Radical Equations and Inequalities
- The Rectangular Coordinate Plane
- The Complex Coordinate Plane
- Distance and Midpoint Formulas
- Relations and Functions
- Domain and Range
- Function Notation, Function Composition, Operations on Functions
- Graphing Linear Equations
- Linear Equations, Finding the Slope of a Line and Equations of Lines
- Graphing Circles
- Graphing Elementary Functions
- Graphing Transformations
- Solving Systems of Linear Equations in Two Variables
- Solving Systems of Linear Equations in Three Variables
- Solving Word Problems with Linear Systems
- Using Curve Fitting to Find an Equation Through Three Points
- Solving Linear Systems using Gaussian Elimination and Gauss-Jordan Elimination
- Matrix Algebra
- Adding and Subtracting Matrices
- Solving Matrix Equations
- Multiplying a Matrix by a Scalar
- Multiplying Matrices
- Finding the Inverse of a Matrix
- Solving Linear Systems using Matrix Inverses
- Determine if functions are one-to-one using the horizontal line test
- Determine if functions are one-to-one algebraically
- Find the Inverse of a One-to-One Function
- Find the Inverse of a Domain Restricted One-to-One Function
- Graphing the Inverse of a Function
- Graphing an Exponential Function
- Solving Exponential Equations with Like Bases
- Solving Compound Interest Word Problems
- Graphing Logarithmic Functions
- Properties of Logarithms | Condensing Logarithms | Expanding Logarithms
- Change of Base Rule for Logarithms
- Solving Exponential and Logarthimic Equations
- Finding the Vertex Form of a Parabola
- How to Graph a Parabola
- Remainder Theorem
- Using the Remainder Theorem to Test Zeros for a Polynomial Function
- The Factor Theorem
- Using the Factor Theorem to Factor a Polynomial Function Given One Zero
- The Rational Zeros Theorem
- The Fundamental Theorem of Algebra
- The Number of Zeros Theorem
- Writing Polynomial Equations Given Zeros and a Point
- Conjugate Zeros Theorem
- Descartes' Rule of Signs
- Intermediate Value Theorem
- Boundedness Theorem
- Finding the upper and lower bounds for the real zeros of a polynomial function

- Basic Arithmetic (Addition, Subtraction, Multiplication, Division)
- Pre-Algebra (Must Have)
- Basic Algebra (Algebra 1) (Must Have)
- Intermediate Algebra (Algebra 2) (Highly Suggested)

Become a Master of **College Algebra** and** Ace** your next **Exam**! In this course, you will master the concepts of **College Algebra** 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

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

- Students who need a complete understanding of Advanced Algebra
- Students currently enrolled in a College Level Algebra Course
- Students currently enrolled in a Pre-Calculus Course
- Students who need to master Algebra in order to fully prepare for Calculus

In this lesson, we will review how to classify real numbers as natural numbers, whole numbers, integers, rational numbers, or irrational numbers. We will also review the basics of inequality relationships between two numbers using a number line.

In this lesson, we will review the concept of an exponent. We will look at how to use exponents to write the repeated multiplication of the same number. We will explore how to work with exponents that have a negative base. Lastly, we will review the rules used to simplify an expression with more than one operation. This procedure is known formally as the order of operations.

In this lesson, we review how to solve literal equations. A literal equation is one that contains more than one unique variable. When we solve a literal equation, we are solving for a specific variable. Another way to think of this is we are putting our equation in terms of one of the variables.

In this lesson, we will review the imaginary unit i and learn how to simplify the square root of a negative number.

In this lesson, we will learn how to plot a complex number on the complex plane.

In this lesson, we learn how to find the absolute value of a complex number a + bi.