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 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 5Solve an Equation by Factoring Example 6Solve a Real-World Problem by Factoring

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

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

8. Example 3-5b SolveCheck your solutions. Answer:

9. Example 3-6a Architecture Marion 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? ExploreBegin by making a diagram like the one shown to the right, labeling the appropriate dimensions.

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

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

12. Photography Adina 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? Example 3-6b Answer:

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