Dive into a comprehensive 5-hour video series on polynomials, covering five essential topics: characteristics, binomial expansion, real zeros, irrational zeros, and complex zeros. Learn through numerous examples how to compare equations and their graphs, determine end behavior, sketch polynomial graphs, apply the Intermediate Value Theorem, use Pascal's Triangle, find zeros and their multiplicity, write polynomial equations, apply the Remainder Theorem, and utilize Descartes' Rule of Signs. Master key concepts like linear factorization, rational zero test, and the sum and difference of cubes to enhance your understanding of polynomial mathematics.
Overview
Syllabus
Characteristics of Polynomials .
Example 01: Compare the Effects of the Equations & Their Graphs .
Example 02: Compare the Effects of the Equations and Their Graphs .
Example 03: Determine the End Behavior & Write in Math Notation .
Example 04: Sketch the Graph of the Following Polynomials .
Example 05: Determine if the Interval the Polynomial must have a Zero Based on the Intermediate Value Theorem .
Binomial Expansion .
Example 01: Multiply the Following Binomial .
Example 02: Expand out the Following Binomials Using Binomial Expansion and Pascal's Triangle .
Example 03: Find the 3rd Term of the Binomial Expansion .
Example 04: Determine the Zeros, Multiplicity, Y-Intercept, Transformations and Vertex of the Quadratic .
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Real Zeros of Polynomials .
Example 01: Find the Zeros and Their Multiplicity of the Following Polynomials .
Example 02: Find the Zeros and Multiplicity of the Polynomial by Writing the Linear Factorization .
Example 03: Find All the Zeros of the Polynomial and Label the Multiplicity of Each Zero .
Example 04: Write the Equation of a Polynomial .
Example 05: Write the Equation of the Polynomial Given the Following Information .
Irrational Zeros of Polynomials .
Example 01: Find the Zeros of the Polynomial and Then Write the Linear Factorization .
Example 02: Write the Following Problem as a Division and Multiplication Problem, then Find All the Linear Factors .
Example 03: Determine if the Following Expressions are a Factor of the Polynomial .
Example 04: Given the Value K Use the Remainder Theorem to Determine the Remainder .
Example 05: Write the Equation of the Following Polynomial Given the Zeros .
Complex Zeros Of Polynomials .
Example 01: Find the Zeros of the Polynomial and then Write the Linear Factorization .
Example 02: Find the Zeros then Write Linear Factorization .
Example 03: Find All the Zeros of Sum & Difference of Two Cubes .
Example 04: Rational Zero Test of Polynomial .
Example 05: Find the Possible Real Positive, Negative and Complex Zeros Using Descartes Rules of Sign .
Example 06: Write the Equation Using Zeros .
Taught by
Brian McLogan
