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9.2

9.2. Factoring Using the Distributive Property. Greatest Common Factor (GCF)/Distributive Property. Look for the largest common number and/or variables in each term Divide each term by the common terms. Use the Distributive Property to factor . First, find the CGF of 15 x and .

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9.2

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  1. 9.2 Factoring Using the Distributive Property

  2. Greatest Common Factor (GCF)/Distributive Property Look for the largest common number and/or variables in each term Divide each term by the common terms

  3. Use the Distributive Property to factor . First, find the CGF of 15x and . Factor each number. GFC: Rewrite each term using the GCF. Simplify remaining factors. Distributive Property Example 2-1a Circle the common prime factors. Write each term as the product of the GCF and its remaining factors. Then use the Distributive Property to factor out the GCF.

  4. Answer: The completely factored form of is Example 2-1a

  5. Use the Distributive Property to factor . Factor each number. GFC: or Rewrite each term using the GCF. Distributive Property Answer: The factored form of is Example 2-1a Circle the common prime factors.

  6. Use the Distributive Property to factor each polynomial. a. b. Answer: Answer: Example 2-1b

  7. Grouping Steps • Arrange terms in descending order • Separate into groups of 2 in () • Factor the GCF from each group • Factor an additional (-1) if necessary • The terms in () must match • Combine the two GCF into a binomial in () and place it next to the other binomial

  8. Grouping Example

  9. Factor Group terms with common factors. Factor the GCFfrom each grouping. Answer: Distributive Property Example 2-2a

  10. Factor Answer: Example 2-2b

  11. Factor Group terms with common factors. Factor GCF from each grouping. Answer: Distributive Property Example 2-3a

  12. Factor Answer: Example 2-3b

  13. Solve Then check the solutions. If , then according to the Zero Product Property either or Original equation or Set each factor equal to zero. Solve each equation. Answer: The solution set is Example 2-4a

  14. Check Substitute 2 and for x in the original equation. Example 2-4a

  15. Solve Then check the solutions. Example 2-4b Answer: {3, –2}

  16. Solve Then check the solutions. Write the equation so that it is of the form Original equation Subtract from each side. Factor the GCF of 4y andwhich is 4y. Zero Product Property or Solve each equation. Example 2-5a

  17. Answer: The solution set is Check by substituting 0 and for y in the original equation. Example 2-5a

  18. Solve Answer: Example 2-5b

  19. Practice Problems Page 484 Problems 4-15, 16-39, 48-59 (odd)

  20. Practice Problems (Day 2) Page 484 Problems 4-15, 16-39, 48-59 (even)

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