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Mastering Polynomial Factoring Using the Boston Method

In this lesson, students will learn how to factor quadratic trinomials of the form ax² + bx + c using the Boston Method. The focus will be on explaining the steps in writing, alongside practical examples and mixed practice exercises. Key learning targets include multiplying binomials, identifying the greatest common factors (GCF), and factoring polynomials. This comprehensive lesson aims to deepen understanding of polynomial factoring and equip students with the necessary skills to solve quadratic equations efficiently.

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Mastering Polynomial Factoring Using the Boston Method

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  1. Algebra 1 8.4 Factoring Boston Method!

  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 ax² + bx + c. Essential Question: How are GCFs used to factor polynomials?

  3. Warm-up

  4. Review Multiply Binomials Multiply the Binomials

  5. Boston Method • Boston Method • If a1: ax2 + bx + c • 1) Multiply a and c. • 2) Rewrite in the form x2 + bx + (ac) • 3) Factor • 4) Divide by a • 5) Simplify • 6) Bring the denominator in front of the x.

  6. Boston Method MixedPractice! a. 4y2 – 4y – 3 b. 2x2 + 7x + 3

  7. Boston Method MixedPractice! c. 3k2 + 32k – 11 d. 6x2 + 7x – 3

  8. More Practice: Factoring ax² + bx + c when c is positive. Factor each trinomial. Check your answer. A. 2x² + 11x + 12 B. 5x² – 14x + 6

  9. More Practice: Factoring ax² + bx + c when c is positive. Factor each trinomial. Check your answer. C. 6x² + 17x + 5 D. 9x² – 15x + 4

  10. More Practice: Factoring ax² + bx + c when c is positive. Factor each trinomial. Check your answer. E. 3x² + 13x + 12F. 2x² + 17x + 21G. 3x² – 16x + 16

  11. More Practice: Factoring ax² + bx + c when c is negative A. 4x² + 7x – 2 B. 4x² + 19x – 5

  12. More Practice: Factoring ax² + bx + c when c is negative C. 2x² – 7x – 15 D. 6x² + 7x – 3

  13. More Practice: Factoring ax² + bx + c when c is negative E. 4x² – x – 3 F. 3x² + 11x – 4 G. 2x² + 9x – 18

  14. More Practice: Factoring ax² + bx + c when a is negative A. -2x² – 15x – 7 B. -6x² – 17x – 12

  15. More Practice: Factoring ax² + bx + c when a is negative C. -3x² – 17x – 10 D. -2x² – 5x – 3

  16. Lesson Quiz

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