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Mastering Polynomial Factoring: Understanding Quadratic Trinomials

In this lesson, students will learn how to factor quadratic trinomials of the form x² + bx + c using the Product-Sum method. They will explain the process of factoring polynomials in writing, and explore the importance of the Greatest Common Factor (GCF) in simplifying expressions. The session includes warm-up exercises, multiple examples of factoring trinomials (including cases where c is negative), and evaluating polynomials to confirm the correctness of factored forms. Students will reinforce their understanding through interactive quizzes and graphic organizers.

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Mastering Polynomial Factoring: Understanding Quadratic Trinomials

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Presentation Transcript

  1. Algebra 1 8.3 Factoring Product Sum Methode

  2. Learning Targets • Language Goal: Students will be able to explain using writing how to factor polynomials. • Math Goal: Students will be able to factor quadratic trinomials of the form x² + bx + c. • Essential Question: How are GCFs used to factor polynomials?

  3. Warm-up

  4. Foiling Review Multiply the binomials

  5. To factor a quadratic trinomial of the form find two factors of c whose sum is b To factor look for factors of 18 whose sum is 9.

  6. Example 2: Factoring Factor each trinomial. Check your answer. A. B.

  7. Example 2: Factoring Factor each trinomial. Check your answer. C. D.

  8. Example 2: Factoring Factor each trinomial. Check your answer. E. F.

  9. Example 2: Factoring Factor each trinomial. Check your answer. H.

  10. Example 3: Factoring when c is negative Factor each trinomial. Check your answer. A.B.

  11. Example 3: Factoring when c is negative Factor each trinomial. Check your answer. C.D.

  12. Example 3: Factoring when c is negative Factor each trinomial. Check your answer. E. F.H.

  13. Example 4: Evaluating Polynomials A. Factor n² + 11n + 24. Show that the original polynomial and the factored form have the same value for n = 0, 1, 2, 3, and 4.

  14. Example 4: Evaluating Polynomials B. Factor n² - 7n + 10. Show that the original polynomial and the factored form have the same value for n = 0, 1, 2, 3, and 4.

  15. Example 4: Evaluating Polynomials C. Factor y² + 10y + 21. Show that the original polynomial and the factored form have the same value for y = 0, 1, 2, 3, and 4.

  16. Graphic Organizer

  17. Lesson Quiz

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