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6.1 Factoring Polynomials

This guide covers the process of finding a common factor across all terms in a polynomial. It explains the concept of monomials, the significance of the Greatest Common Factor (GCF), and how to streamline polynomials by removing common factors from each term. You will learn how to identify the largest factor common to all polynomial terms and address problems involving relatively prime polynomials. A step-by-step approach with practical examples ensures clarity for students studying polynomial factoring.

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6.1 Factoring Polynomials

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  1. 6.1Factoring Polynomials Standard 11.0: Find a common factor to all of the terms in a polynomial

  2. Monomial Polynomial Factor Greatest Common Factor (GCF) One Term A monomial or sum of monomials Removing common factors from each term of a polynomial The largest factor that occurs in each term. Vocabulary

  3. #1 Factor GCF: Divide by the GCF Check

  4. #2 Factor GCF: Divide by the GCF: Check

  5. #3 Factor GCF: Divide by the GCF: Check

  6. #4 Factor GCF: Divide by the GCF: Check

  7. #5 Factor GCF: Check

  8. Relatively Prime Vocabulary • Polynomials that have no common factors.

  9. #6 Are the following relatively prime? What is the largest factor common to both polynomials? No

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