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Lesson 3 Contents

Lesson 3 Contents. Example 1 b and c Are Positive Example 2 b Is Negative and c Is Positive Example 3 b Is Positive and c Is Negative Example 4 b Is Negative and c Is Negative Example 5 Solve an Equation by Factoring Example 6 Solve a Real-World Problem by Factoring. Factor.

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Lesson 3 Contents

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  1. Lesson 3 Contents Example 1b and c Are Positive Example 2b Is Negative and c Is Positive Example 3b Is Positive and c Is Negative Example 4b Is Negative and c Is Negative Example 5Solve an Equation by Factoring Example 6Solve a Real-World Problem by Factoring

  2. Factor In this trinomial, and You need to find the two numbers whose sum is 7 and whose product is 12. Make an organized list of the factors of 12, and look for the pair of factors whose sum is 7. Write the pattern. and Answer: Example 3-1a The correct factors are 3 and 4.

  3. F O I L FOIL method Simplify. Example 3-1a Check You can check the result by multiplying the two factors.

  4. Factor Answer: Example 3-1b

  5. Factor In this trinomial, and This means is negative and mn is positive. So m and n must both be negative. Therefore,make a list of the negative factors of 27, and look for the pair whose sum is –12. Write the pattern. Answer: and Example 3-2a The correct factors are –3 and –9.

  6. Check You can check this result by using a graphing calculator. Graph andon the same screen. Since only one graph appears, the two graphs must coincide. Therefore, the trinomial has been factored correctly. Example 3-2a

  7. Factor Answer: Example 3-2b

  8. Factor In this trinomial, and Thismeans is positive and mn is negative, so either m or n is negative, but not both. Therefore,make a list of the factors of –18 where one factorof each pair is negative. Look for the pair of factors whose sum is 3. Example 3-3a The correct factors are –3 and 6.

  9. Write the pattern. and Answer: Example 3-3a

  10. Factor Answer: Example 3-3b

  11. Factor Since and is negative and mn is negative. So either m or n is negative, but not both. Example 3-4a The correct factors are 4 and –5.

  12. Write the pattern. and Answer: Example 3-4a

  13. Factor Answer: Example 3-4b

  14. Solve Check your solutions. Original equation Rewritethe equation so that one side equals 0. or Factor. Zero Product Property Solve each equation. Answer: The solution is Example 3-5a

  15. Example 3-5a Check Substitute –5 and 3 for x in the original equation.

  16. Solve Check your solutions. Answer: Example 3-5b

  17. Example 3-6a ArchitectureMarion has a small art studio measuring 10 feet by 12 feet in her backyard. She wants to build a new studio that has three times the area of the old studio by increasing the length and width by the same amount. What will be the dimensions of the new studio? Explore Begin by making a diagram like the one shown to the right, labeling the appropriate dimensions.

  18. Write the equation. Solve Multiply. Plan Let the amount added to each dimension of the studio. old area Subtract 360 from each side. Example 3-6a The new length times the new width equals the new area.

  19. Factor. Zero Product Property or Solve each equation. Examine The solution set is Only 8 is a valid solution, since dimensions cannot be negative. Answer: The lengthof the new studio should be or 20 feet and the new width should be or 18 feet. Example 3-6a

  20. PhotographyAdina has a photograph. She wants to enlarge the photograph by increasing the length and width by the same amount. What dimensions of the enlarged photograph will be twice the area of the original photograph? Answer: Example 3-6b

  21. End of Lesson 3

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