Irrational Zeros of Polynomials - Polynomials - Pre-Calculus

Discover how to determine irrational zeros of polynomial equations through factoring, long division, and synthetic division in this comprehensive 57-minute pre-calculus lesson. Learn to apply the remainder and factor theorems, and master writing polynomial equations given their zeros. Explore various techniques including zeros without factoring, linear factorization, and understanding division through multiple examples. Gain insights into the relationship between factors and zeros, and practice with real-world applications. Follow along with clearly marked timestamps for each topic, including corrections for minor mistakes. Enhance your polynomial skills with this thorough tutorial designed to make complex concepts accessible and easy to understand.

Intro.
Zeros without Factoring.
Linear Factorization.
Irrational Zeros by Factoring.
Understanding Division (a.).
Understanding Division (b.).
Factors vs. Zeros.
Understanding Division (c.) .
Understanding Division (d.).
Understanding Division (e.).
Understanding Division (e.).
Factor Theorem (Intro).
Factor Theorem (Example #1).
Factor Theorem (Example #2).
Remainder Theorem .
Write the Equation.
Made a mistake. The final zeros should be (1+_√3).
In the synthetic division, final answer is x^2 + 5x + 6.