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 Tags: binomial formula Differentiated Instruction Pacing (43 more) constant Science Inquiry Teacher Edition monomial Inquiry Process distributive property problem solving linear term standard form Assessment Activities Tests Teaching Strategies Quizzes Concept Check and Troubleshooting Teaching Strategies and Tips CK.MAT.ENG.TE.1.Algebra-I.9 Answer Key Answers Common Misconceptions Worksheets zero-product property degree factoring quadratic expressions leading coefficient term polynomials Solution Key binomial quadratic term Problem Sets Enrichment coefficients cubic term simplifying polynomials trinomial leading term Testing perfect square trinomial square of a binomial Solutions greatest common monomial factor degree of polynomials Categories: mathematics Algebra Grades: 9 , 10 Date Created: Feb 22, 2012 Last Modified: Nov 15, 2012 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.