Synthetic division is a **step-by-step method** for dividing polynomials by linear factors. This technique simplifies the process of polynomial long division, especially when dealing with monic linear divisors. The transcript provides a comprehensive overview of synthetic division, including its definition, application, and examples.

Key points:

- Synthetic division is used for dividing polynomials by monic linear divisors (x - c)
- It's a shortcut method that reduces the work compared to traditional long division
- The process involves arranging coefficients and performing simple arithmetic operations
- Synthetic division is particularly useful for finding polynomial roots and factoring