1 / 29

FOIL Method and Factoring Quadratics

This lesson covers the FOIL method for multiplying binomials and factoring quadratics. It includes examples of translating sentences into equations, using the zero product property, factoring GCF, perfect squares and differences of squares, and factoring trinomials. Real-world examples of solving equations by factoring are also provided.

stefaniek
Download Presentation

FOIL Method and Factoring Quadratics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Splash Screen

  2. Five-Minute Check (over Lesson 4–2) CCSS Then/Now New Vocabulary Key Concept: FOIL Method for Multiplying Binomials Example 1: Translate Sentences into Equations Concept Summary: Zero Product Property Example 2: Factor GCF Example 3: Perfect Squares and Differences of Squares Example 4: Factor Trinomials Example 5: Real-World Example: Solve Equations by Factoring Lesson Menu

  3. Use the related graph of y = x2 – 4 to determine its solutions. A. 4, –4 B. 3, –2 C. 2, 0 D. 2, –2 5-Minute Check 1

  4. Use the related graph of y = –x2 – 2x + 3 to determine its solutions. A. –3, 1 B. –3, 3 C. –1, 3 D. 3, 1 5-Minute Check 2

  5. Solve –2x2 + 5x = 0. If exact roots cannot be found, state the consecutive integers between which the roots are located. A. 0 B. 0, between 2 and 3 C. between 1 and 2 D. 2, –2 5-Minute Check 3

  6. Which term is not another name for a solution to a quadratic equation? A. zero B.x-intercept C. root D. vertex 5-Minute Check 5

  7. Content Standards A.SSE.2 Use the structure of an expression to identify ways to rewrite it. F.IF.8.a Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. Mathematical Practices 2 Reason Abstractly and quantitatively. CCSS

  8. You found the greatest common factors of sets of numbers. • Write quadratic equations in intercept form. • Solve quadratic equations by factoring. Then/Now

  9. factored form • FOIL method Vocabulary

  10. Concept

  11. Replace p withand q with –5. Translate Sentences into Equations (x – p)(x – q) = 0 Write the pattern. Simplify. Use FOIL. Example 1

  12. Answer: Translate Sentences into Equations Multiply each side by 2 so b and c are integers. Example 1

  13. A. ans B. ans C. ans D. ans Example 1

  14. Concept

  15. y = 0 Solve each equation. Answer: Factor GCF A.Solve 9y2 + 3y = 0. 9y2 + 3y = 0 Original equation 3y(3y) + 3y(1) = 0 Factor the GCF. 3y(3y + 1) = 0 Distributive Property 3y = 0 3y + 1 = 0 Zero Product Property Example 2

  16. Factor GCF B.Solve 5a2 – 20a = 0. 5a2 – 20a = 0 Original equation 5a(a) – 5a(4) = 0 Factor the GCF. 5a(a – 4) = 0 Distributive Property 5a = 0 a – 4 = 0 Zero Product Property a = 0 a = 4 Solve each equation. Answer:0, 4 Example 2

  17. Solve 12x – 4x2 = 0. A. 3, 12 B. 3, –4 C. –3, 0 D. 3, 0 Example 2

  18. Perfect Squares and Differences of Squares A.Solve x2 – 6x + 9 = 0. x2 = (x)2; 9 = (3)2 First and last terms are perfect squares. 6x = 2(x)(3) Middle term equals 2ab. x2 – 6x + 9 is a perfect square trinomial. x2 + 6x + 9 = 0 Original equation (x – 3)2 = 0 Factor using the pattern. x – 3 = 0 Take the square root of each side. x = 3 Add 3 to each side. Answer:3 Example 3

  19. Perfect Squares and Differences of Squares B.Solve y2 = 36. y2 = 36 Original equation y2 – 36 = 0 Subtract 36 from each side. y2 – (6)2 = 0 Write in the form a2 – b2. (y + 6)(y – 6) = 0 Factor the difference of squares. y + 6 = 0 y – 6 = 0 Zero Product Property y = –6 y = 6 Solve each equation. Answer:–6, 6 Example 3

  20. Solve x2 – 16x + 64 = 0. A. 8, –8 B. 8, 0 C. 8 D. –8 Example 3

  21. Factor Trinomials A.Solve x2 – 2x – 15 = 0. ac = –15 a = 1, c = –15 Example 4

  22. Factor Trinomials x2 – 2x – 15 = 0 Original equation x2 + mx + px – 15 = 0 Write the pattern. x2 + 3x – 5x – 15 = 0 m = 3 and p = –5 (x2 + 3x) – (5x + 15) = 0 Group terms with common factors. x(x + 3) – 5(x + 3) = 0 Factor the GCF from each grouping. (x – 5)(x + 3) = 0 Distributive Property x – 5 = 0 x + 3 = 0 Zero Product Property x = 5 x = –3 Solve each equation. Answer:5, –3 Example 4

  23. Factor Trinomials B.Solve 5x2 + 34x + 24 = 0. ac = 120 a = 5, c = 24 Example 4

  24. x = –6 Solve each equation. Factor Trinomials 5x2 + 34x + 24 = 0 Original equation 5x2 + mx + px + 24 = 0 Write the pattern. 5x2 + 4x + 30x + 24 = 0 m = 4 and p = 30 (5x2 + 4x) + (30x + 24) = 0 Group terms with common factors. x(5x + 4) + 6(5x + 4) = 0 Factor the GCF from each grouping. (x + 6)(5x + 4) = 0 Distributive Property x + 6 = 0 5x + 4 = 0 Zero Product Property Example 4

  25. Answer: Factor Trinomials Example 4

  26. A. B. C. D. A. Solve 6x2 – 5x – 4 = 0. Example 4

  27. B.Factor 3s2 – 11s – 4. A. (3s + 1)(s – 4) B. (s + 1)(3s – 4) C. (3s + 4)(s – 1) D. (s – 1)(3s + 4) Example 4

  28. End of the Lesson

  29. Page 242 #18 - 42

More Related