Synthetic division is a method for dividing polynomials that is faster and more efficient than long division. This technique is particularly useful when dividing a polynomial by a linear factor. The process involves setting up a compact arrangement of the coefficients and performing simple arithmetic operations.

Highlight: Synthetic division is a streamlined method for polynomial division, especially effective when dividing by linear factors (x - a).

The method follows these general steps:

1. Arrange the polynomial in descending order of degree
2. Set up the division using only the coefficients
3. Bring down the first coefficient
4. Multiply the result by the divisor and add to the next coefficient
5. Repeat step 4 until all coefficients are processed

Example: For (x³-2x²-5x+6) ÷ (x-3), the synthetic division process yields x²+3x+1 as the quotient with a remainder of 0.

Synthetic division not only simplifies the division process but also helps in finding roots of polynomials and factoring higher-degree polynomials.

Vocabulary: Coefficients are the numerical factors of the variables in a polynomial expression.

This method is an essential tool in algebra and calculus, providing a quick way to perform polynomial division and analyze polynomial behavior.