About Course

Gain complete mastery over polynomial expressions and their operations in this focused mini-course. You’ll begin by dissecting algebraic expressions—learning to name every part, classify by term count and degree, and recognize the structure beneath the symbols. From there, you’ll learn to combine like terms and simplify complex sums, then move on to multiplying polynomials of all shapes and sizes. Finally, you’ll divide with confidence: handling monomial quotients, performing long division on higher-degree polynomials, and breaking down rational expressions through partial-fraction decomposition. With clear, step-by-step examples, targeted practice sets, and real-world applications, you’ll build the skills to tackle any polynomial challenge.

What Will You Learn?

  • Precisely identify and classify algebraic expressions by term count and degree
  • Combine like terms to simplify any polynomial expression
  • Multiply monomials and polynomials using the distributive principle and FOIL
  • Perform long division on polynomials to find quotients and remainders
  • Break down rational expressions into partial fractions for advanced applications

Course Content

1. Algebraic Expressions & Classification
Understand what makes up an algebraic expression—variables, coefficients, constants and operators—and learn to classify them by number of terms (monomials, binomials, trinomials, polynomials) and by degree. This foundational knowledge ensures you can read, interpret, and categorize any expression you meet.

  • 1.1 Parts of an Expression: Variables, Coefficients & Constants
  • 1.2 Classification by Term Count: Mono-, Bi-, Tri- & Polynomials
  • 1.3 Degree of an Expression & Its Significance

2. Like Terms & Simplification
Discover how to spot terms that share the same variable part and combine them to simplify expressions. You’ll practice grouping, adding, and subtracting like terms until complex expressions collapse into their simplest form.

3. Multiplication of Polynomials
Learn efficient methods for multiplying monomials, binomials, trinomials, and beyond. Starting with single-term products, you’ll advance to two-term and three-term multiplications, mastering FOIL and the distributive principle so you can expand any polynomial product accurately.

4. Division of Polynomials
Build confidence dividing by peeling off factors one piece at a time. You’ll begin with simple monomial quotients, then learn long-division techniques for any two polynomials. Finally, you’ll decompose complex rational expressions into simpler pieces via partial-fraction methods—an indispensable tool for later calculus work.