Precalculus Foundations: Polynomials and Rational Functions

Many students struggle with calculus not because of the new concepts, but because their algebraic foundation is shaky. Understanding polynomial and rational functions is the absolute key to unlocking advanced mathematical reasoning, scientific modeling, and higher-level calculus. This text-based course helps you build a rock-solid mathematical foundation. You will move from basic algebraic definitions to analyzing complex functions, equipping you with the analytical skills needed for advanced studies and modern technical applications. What you'll learn: - Understand the fundamental properties, degrees, and end behaviors of polynomial functions - Apply polynomial division techniques, including long division and synthetic division, to find real and complex roots - Analyze rational functions by determining domains, vertical and horizontal asymptotes, and removable discontinuities - Solve complex polynomial and rational inequalities using sign charts and algebraic methods - Explore real-world modeling applications where these mathematical structures represent modern physical and economic systems Your learning journey starts with essential terminology and foundational definitions before guiding you step-by-step through advanced algebraic manipulations. You will reinforce each concept through clear written explanations, detailed mathematical proofs, and structured practice exercises. This course is designed for students, self-learners, and aspiring technical professionals who want to master precalculus concepts. No advanced mathematical background is required; a basic understanding of introductory algebra is the only prerequisite. Start building your mathematical confidence today.