9.5: Factoring Quadratic Expressions Created by: CK-12 Algebra I Teacher's Edition TE Factoring Polynomials Edit Review Was this helpful? Submit Review Skip Review Cancel Read Resources Details Learning Objectives At the end of this lesson, students will be able to: Write quadratic equations in standard form. Factor quadratic expressions for different coefficient values. Factor when . Vocabulary Terms introduced in this lesson: quadratic polynomial quadratic trinomials Teaching Strategies and Tips In this lesson, students learn to factor quadratic polynomials according to the signs of and : . See Examples 1-4. Additional Examples: Factor. a. . Answer: b. . Answer: c. . Answer: . See Examples 5 and 6. Additional Examples: Factor. a. . Answer: b. . Answer: c. . Answer: . See Examples 7-9. Additional Examples: Factor. a. . Answer: b. . Answer: c. . Answer: . See Example 10. Additional Examples: Factor. a. . Answer: b. . Answer: c. . Answer: Allow students to infer that if , then the factorization will be either of the form or (same signs). If , then use the form (different signs). See summary at the end of the lesson for a list of procedures and examples for each case. Emphasize that factoring is the reverse of multiplication. Use an example such as in which the binomials are expanded one step at a time to motivate factoring. Demonstrate that factoring is equivalent to putting squares and rectangles back together into larger rectangles. Example: Multiply. . Solution. The diagram shows that . Observe that it also shows how to factor . Suggest that students stop listing the possible products for after the correct choice is evident. Error Troubleshooting General Tip: For quadratic trinomials with , remind students to factor from every term. Remind students to include it in their final answer. Image Attributions Description No description available here... Authors: CK12 Editor Categories: mathematics Algebra Grades: 9 , 10 Date Created: Feb 22, 2012 Last Modified: Apr 29, 2014 You can only attach files to None which belong to you If you would like to associate files with this None, please make a copy first.