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Presentation. AA20 Factor algebraic expressions completely, including trinomials with a lead coefficient of one (after factoring a GCF). What we want students to do. Factor quadratic trinomials of the form. What students can already do. Factoring quadratic trinomials of the form.

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  1. Presentation AA20 Factor algebraic expressions completely, including trinomials with a lead coefficient of one (after factoring a GCF)

  2. What we want students to do Factor quadratic trinomials of the form

  3. What students can already do Factoring quadratic trinomials of the form

  4. What do we want students to do? • Factor quadratic trinomials of the form • Write the factorization of numbers. • Factor polynomials by using the greatest common factor (GCF). • Find the GCF of monomials. • Write the prime factorization of numbers.

  5. What concepts do students need to know? • Distributive Property • Area of rectangles • Combine like terms • Laws of exponents-multiplication • Factoring quadratic trinomials by guess and check

  6. What questions need to be answered? • How is factoring a trinomial in the form similar to factoring a trinomial in the form ? How is it different? • What is true about the signs of the factors of the last term if the middle term is positive? negative? • What should the sum of the inner and outer products be? • What do you know about the binomials in the factored expression when the constant term in the trinomial is negative? • How do you know which term is the leading coefficient? • What is the advantage to factoring out -1 in the first step?

  7. Aim How do we factor ?

  8. Simplify 1. 2. Find the GCF of each pair of monomials. 3. and 4. and Factor each trinomial 5. 6. Do Now

  9. Lesson Plan Topic (NYS) Factoring ax² + bx + c (AA20) Aim How do we factor ax² + bx + c ? Do Now! • Distribute monomials using multiplication • Find the GCF of monomials • Factoring x² + bx + c Mini-Lesson Factoring ax² + bx + c when c is positive Factoring ax² + bx + c when c is negative • Use Distributive Property twice to check answer • Law of exponents-multiplication • When b is negative and c is positive, the factors of c are both negative. Factoring ax² + bx + c when a is negative • When you factor out -1 in an early step, you must carry it through the rest of the steps. Guided practice HOLT 8.4 p548 -551

  10. Investigation • Answer student questions • Facilitate critical thinking • Keep students on task Share & Summarize • Selected student sharing • Discuss solutions using accountable talk • Identify alternate solutions & perspectives Closure • Answer Aim • Assign Homework • Check for understanding Homework HOLT p535 Qs:1, 12, 15, 21; p544 Qs:1, 4, 10; p552 Qs:1, 3,5, 7, 13 and 19. Multicultural Accommodations • Shift to directed instruction as needed • Reframe problems using familiar context as needed • Read instructions & problems aloud to ESL students Materials/Handouts None

  11. Example Questions • Example 1 Factoring when c is positive Factor each trinomial. Check your answer. • 2x² + 11x + 12 • 5x² – 14x + 8 Try this: 1. 6x² + 17x +5 2. 9x² - 15x + 4 3. 3x² + 13x + 12

  12. Example 2 Factoring when c is negative Factor each trinomial. Check your answer. • 4y² + 7y – 2 • 4x² + 19x – 5 • 2x² - 7x – 15 Try this: 1. 6x² + 7x – 3 2. 4n² - n - 3

  13. Example 3 Factoring when a is negative Factor -2x² - 15x – 7 Try this: 1. -6x² - 17x – 12 2. -3x² - 17x - 10

  14. Vocabulary Math each term on the left with a definition on the right. 1. binomial A. the product of any number and a whole number 2. Factor B. a polynomial with two terms 3. Multiple C. a number that is multiplied by another number to get a product 4. Prime number D. a whole number greater than 1 that has exactly two factors, itself and 1

  15. Summary Factor factors of a factors of c a1 c1 a2 c2 a1 * a2 = a c1 * c2 = c a1 * c2 + a2 * c1 = b

  16. Regents Exam Questions by topicQuadratics: Factoring Polynomialswww.jmap.org

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