College Algebra

As a foundational university-level course, College Algebra builds upon high school algebra concepts to provide a deeper understanding of functions and their applications. The curriculum is centered on the rigorous study of various function types—including polynomial, rational, exponential, and logarithmic—with a strong emphasis on analyzing their graphs, properties, and transformations. Students develop critical problem-solving skills by solving complex equations and inequalities, modeling real-world phenomena, and establishing the essential groundwork required for calculus and other quantitative fields.

  1. Foundational Algebraic Concepts
    1. The Real Number System
      1. Definition of Real Numbers
        1. Subsets of Real Numbers
          1. Natural Numbers
            1. Whole Numbers
              1. Integers
                1. Rational Numbers
                  1. Irrational Numbers
                  2. Properties of Real Numbers
                    1. Commutative Property
                      1. Addition
                        1. Multiplication
                        2. Associative Property
                          1. Addition
                            1. Multiplication
                            2. Distributive Property
                              1. Identity Property
                                1. Additive Identity
                                  1. Multiplicative Identity
                                  2. Inverse Property
                                    1. Additive Inverse
                                      1. Multiplicative Inverse
                                    2. Order of Operations
                                      1. PEMDAS/BODMAS Rules
                                        1. Nested Parentheses
                                          1. Evaluating Complex Expressions
                                          2. Absolute Value
                                            1. Definition and Notation
                                              1. Properties of Absolute Value
                                                1. Solving Absolute Value Expressions
                                                  1. Distance Interpretation
                                                2. Exponents and Radicals
                                                  1. Integer Exponents
                                                    1. Definition and Notation
                                                      1. Laws of Exponents
                                                        1. Product Rule
                                                          1. Quotient Rule
                                                            1. Power Rule
                                                              1. Zero Exponent
                                                                1. Negative Exponents
                                                                2. Simplifying Expressions with Exponents
                                                                3. Scientific Notation
                                                                  1. Writing Numbers in Scientific Notation
                                                                    1. Operations with Scientific Notation
                                                                      1. Multiplication and Division
                                                                        1. Addition and Subtraction
                                                                        2. Applications in Real-World Contexts
                                                                        3. Rational Exponents
                                                                          1. Definition and Notation
                                                                            1. Converting between Radicals and Rational Exponents
                                                                              1. Properties of Rational Exponents
                                                                                1. Simplifying Expressions with Rational Exponents
                                                                                2. Radicals
                                                                                  1. Definition and Notation
                                                                                    1. Simplifying Radicals
                                                                                      1. Prime Factorization Method
                                                                                        1. Product and Quotient Rules for Radicals
                                                                                        2. Operations with Radicals
                                                                                          1. Addition and Subtraction
                                                                                            1. Multiplication and Division
                                                                                            2. Rationalizing Denominators
                                                                                              1. Monomial Denominators
                                                                                                1. Binomial Denominators
                                                                                                2. Higher-Order Radicals
                                                                                              2. Polynomials
                                                                                                1. Terminology
                                                                                                  1. Monomials
                                                                                                    1. Binomials
                                                                                                      1. Trinomials
                                                                                                        1. Degree of a Polynomial
                                                                                                          1. Coefficients
                                                                                                            1. Leading Term and Leading Coefficient
                                                                                                              1. Constant Term
                                                                                                                1. Standard Form
                                                                                                                2. Adding and Subtracting Polynomials
                                                                                                                  1. Combining Like Terms
                                                                                                                    1. Vertical Format
                                                                                                                      1. Horizontal Format
                                                                                                                      2. Multiplying Polynomials
                                                                                                                        1. Distributive Property
                                                                                                                          1. FOIL Method
                                                                                                                            1. Multiplying Larger Polynomials
                                                                                                                              1. Area Model Method
                                                                                                                              2. Special Products
                                                                                                                                1. Square of a Binomial
                                                                                                                                  1. Product of a Sum and Difference
                                                                                                                                    1. Cube of a Binomial
                                                                                                                                      1. Higher-Order Special Products
                                                                                                                                      2. Dividing Polynomials
                                                                                                                                        1. Dividing by Monomials
                                                                                                                                          1. Long Division Method
                                                                                                                                            1. Synthetic Division
                                                                                                                                          2. Factoring Polynomials
                                                                                                                                            1. Identifying Common Factors
                                                                                                                                              1. Factoring out the Greatest Common Factor
                                                                                                                                                1. Factoring by Grouping
                                                                                                                                                  1. Factoring Trinomials
                                                                                                                                                    1. Trinomials with Leading Coefficient 1
                                                                                                                                                      1. Trinomials with Leading Coefficient not 1
                                                                                                                                                        1. Trial and Error Method
                                                                                                                                                          1. AC Method
                                                                                                                                                          2. Factoring Special Forms
                                                                                                                                                            1. Difference of Squares
                                                                                                                                                              1. Sum of Cubes
                                                                                                                                                                1. Difference of Cubes
                                                                                                                                                                  1. Perfect Square Trinomials
                                                                                                                                                                  2. Complete Factorization
                                                                                                                                                                    1. Solving Polynomial Equations by Factoring
                                                                                                                                                                      1. Zero Product Property
                                                                                                                                                                        1. Finding All Solutions
                                                                                                                                                                      2. Rational Expressions
                                                                                                                                                                        1. Definition and Notation
                                                                                                                                                                          1. Domain of a Rational Expression
                                                                                                                                                                            1. Identifying Restrictions
                                                                                                                                                                              1. Excluded Values
                                                                                                                                                                              2. Simplifying Rational Expressions
                                                                                                                                                                                1. Reducing to Lowest Terms
                                                                                                                                                                                  1. Factoring Numerator and Denominator
                                                                                                                                                                                  2. Multiplying and Dividing Rational Expressions
                                                                                                                                                                                    1. Multiplying Rational Expressions
                                                                                                                                                                                      1. Dividing Rational Expressions
                                                                                                                                                                                        1. Simplifying Products and Quotients
                                                                                                                                                                                        2. Adding and Subtracting Rational Expressions
                                                                                                                                                                                          1. Same Denominators
                                                                                                                                                                                            1. Different Denominators
                                                                                                                                                                                              1. Finding Least Common Denominator
                                                                                                                                                                                                1. Combining Rational Expressions
                                                                                                                                                                                                2. Simplifying Complex Fractions
                                                                                                                                                                                                  1. Method 1: Simplify Numerator and Denominator Separately
                                                                                                                                                                                                    1. Method 2: Multiply by LCD of All Fractions
                                                                                                                                                                                                    2. Solving Rational Equations
                                                                                                                                                                                                      1. Cross Multiplication
                                                                                                                                                                                                        1. LCD Method
                                                                                                                                                                                                          1. Checking for Extraneous Solutions

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                                                                                                                                                                                                      2. Equations and Inequalities