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Lesson 9.2 Factoring Using the Distributive Property, pg. 481

Lesson 9.2 Factoring Using the Distributive Property, pg. 481. Objectives : To factor a polynomial using the Distributive Property. To solve quadratic equations of the form ax² + bx = 0. Vocabulary.

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Lesson 9.2 Factoring Using the Distributive Property, pg. 481

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  1. Lesson 9.2Factoring Using the Distributive Property, pg. 481 Objectives: To factor a polynomial using the Distributive Property. To solve quadratic equations of the form ax² + bx = 0.

  2. Vocabulary • Factoring: to express a polynomial as the product of monomials and polynomials. • Factoring by grouping: the use of the Distributive Property to factor some polynomials having four or more terms.

  3. Review from Chapter 8 2a(6a + 8) = 2a(6a) + 2a(8) = 12a² + 16a You can reverse this process to express a polynomial as the product of a monomial factor and a polynomial factor. 12a² + 16a = 2a(6a) + 2a(8) = 2a(6a + 8) = 2a(2)(3a + 4) = 4a (3a + 4) Not completely factored completely factored

  4. 15x + 25x² 2. Ex. 1: Factoring using the Distributive Property

  5. 3. 16xz – 40xz² 4. 2a³b² + 8ab + 16a²b³

  6. 5. 9x² + 36x 6. 24m²np² + 36m²n²p Your turn…..

  7. 4ab + 8b + 3a + 6 Factor by Grouping: • There are four or more terms. • Terms with common factors can be grouped together. • The two common factors are identical or are additive inverses of each other. Ex. (4ab + 8b) + (3a + 6) group terms with common factors 4b(a + 2) + 3(a + 2) factor within the grouping (a + 2)(4b + 2) factor within entire polynomial

  8. 2xy + 7x – 2y - 7 2. 15a – 3ab + 4b - 20 Ex. 2: Factoring by grouping.

  9. 3. 5y² - 15y + 4y - 12 4. 5c – 10c² + 2d – 4cd

  10. 5. 18x² - 30x – 3x + 5 6. 2my + 7x + 7m + 2xy Your turn…

  11. Zero Product Property • If the product of two factors is 0, then at least one of the factors must be 0. If ab = 0, then a = 0 or b = 0 or both a and b equal zero.

  12. (x – 2)(4x – 1) = 0 2. h(h+ 5) = 0 Ex. 3: Solve an equation in factored form.

  13. 3. (n - 4)(n + 2) = 0

  14. 1. 8p² - 4p = 0 2. 2z² + 20z = 0 Ex. 4: Solve each equation.

  15. 3. 5m – 3m² = 0

  16. 1. 7d² = 6x 2. 20x² = -15x Ex. 5: Solving equations by factoring. Note: If an equation can be written in the ab = 0 form, then the ZERO Product Property can be used.

  17. 3. 14x² = -21x

  18. Summary • Factoring a polynomial means to find its completely factored form by dividing each term by the GCF and then multiplying the result by the GCF. • The GCF is the greatest number that is a factor of both original number. • Factor by grouping when a polynomial has four or more terms with no common factors. • Use the Zero Product Property to solvean equation by factoring. Simply take each factor and set them both equal to zero and solve. NBA #2, page 484, problems 16-58 even, omit 42, 44, 46

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