3.3B Synthetic Division
This section introduces the concept of synthetic division, a simplified method for dividing polynomials by linear factors. It begins by defining key terms and progresses to demonstrate the technique through examples.
A. Linear Polynomials
Linear polynomials are defined as polynomials of the form ax + b, where a ≠ 0.
Example: 3x - 1, 2x - 5, and 3x - 1 are linear polynomials.
B. Monic Polynomials
Monic polynomials are polynomials with a leading coefficient of 1.
Example: x³ + 5x² - 2x - 1, x² - 3x² - 2, and x + b are monic polynomials.
C. Monic Linear Polynomials
Monic linear polynomials are both linear and monic, taking the form x - c.
Example: x + 5, x - 2, and x + 3 are monic linear polynomials.
Highlight: All monic linear polynomials can be written as x - c, where c can be positive, negative, or zero.