2. Welcome to Interactive Chalkboard Algebra 1 Interactive Chalkboard Copyright © by The McGraw-Hill Companies, Inc. Send all inquiries to: GLENCOE DIVISION Glencoe/McGraw-Hill 8787 Orion Place Columbus, Ohio 43240

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4. Contents Lesson 9-1Factors and Greatest Common Factors Lesson 9-2Factoring Using the Distributive Property Lesson 9-3Factoring Trinomials: x 2 + bx + c Lesson 9-4Factoring Trinomials: ax 2 + bx + c Lesson 9-5Factoring Differences of Squares Lesson 9-6Perfect Squares and Factoring

5. Lesson 4 Contents Example 1Factor ax 2 + bx + c Example 2Factor When a, b, and c Have a Common Factor Example 3Determine Whether a Polynomial Is Prime Example 4Solve Equations by Factoring Example 5Solve Real-World Problems by Factoring

6. Example 4-1a Factor In this trinomial,and You need to find two numbers whose sum is 27 and whose product is or 50. Make an organized list of factors of 50 and look for the pair of factors whose sum is 27. Factors of 50 Sum of Factors 1, 50 2, 25 51 27 The correct factors are 2 and 25.

7. Example 4-1a Write the pattern. Group terms with common factors. Factor the GCF from each grouping. and Answer: Distributive Property Check You can check this result by multiplying the two factors. FOIL method FOIL Simplify.

8. Example 4-1a Factor Answer:

9. The correct factors are –4, –18. Example 4-1b Factor In this trinomial,and Since b is negative, is negative. Since c is positive, mn is positive. So m and n must both be negative. Therefore, make a list of the negative factors of or 72, and look for the pair of factors whose sum is –22. –73 –38 –27 –22 –1, –72 –2, –36 –4, –24 –4, –18 Sum of Factors Factors of 72

10. Example 4-1b Write the pattern. and Group terms with common factors. Factor the GCF from each grouping. Distributive Property Answer:

11. Example 4-1b a. Factor b. Factor Answer:

12. Example 4-2a 9696 1, 8 2, 4 Sum of Factors Factors of 8 Factor Notice that the GCF of the terms, and 32 is 4. When the GCF of the terms of a trinomial is an integer other than 1, you should first factor out this GCF. Distributive Property Now factorSince the lead coefficient is 1, find the two factors of 8 whose sum is 6. The correct factors are 2 and 4.

13. Example 4-2a Answer: So,Thus, the complete factorization ofis

14. Example 4-2b Factor Answer:

15. Example 4-3a 14 –14 2 –2 –1, 15 1, –15 –3, 5 3, –5 Sum of Factors Factors of –15 Factor In this trinomial,and Since b is positive, is positive. Since c is negative, mn is negative, so either m or n is negative, but not both. Therefore, make a list of all the factors of 3(–5) or –15, where one factor in each pair is negative. Look for the pair of factors whose sum is 7.

16. Example 4-3a There are no factors whose sum is 7. Therefore, cannot be factored using integers. Answer:is a prime polynomial.

17. Example 4-3b Factor Answer: prime

18. End of Lesson 4

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