Mastering Polynomial Division: Monomials and Long Division

The Organic Chemistry Tutor

This instructional video provides a comprehensive tutorial on dividing polynomials, covering two distinct methods based on the divisor type. The video begins by demonstrating how to divide a polynomial by a monomial (a single term) by separating the expression into individual fractions and simplifying each term using exponent rules. This section builds a foundation for understanding term-wise division before moving to more complex scenarios. The second and larger portion of the video focuses on algebraic long division, used when dividing a polynomial by a binomial (two terms). The instructor walks through the standard algorithm step-by-step: divide, multiply, subtract, and bring down. Key themes include organizing polynomials in descending order, handling negative signs during subtraction, and checking answers by multiplying the quotient and divisor (FOIL method). This resource is highly valuable for high school algebra classrooms. It addresses common student stumbling blocks, such as what to do when a term is missing in the polynomial sequence (using placeholders like 0x) and how to properly format a final answer that includes a remainder. The clear, color-coded handwriting helps visual learners track the movement of numbers and variables throughout the complex multi-step processes.