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Master Factoring Techniques: Polynomial Solutions Simplified

Learn how to factor polynomials efficiently using the Distributive Property and Grouping Methods. Practice with step-by-step examples to enhance your factoring skills. Understand factoring by grouping and zero product property to solve equations effectively.

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Master Factoring Techniques: Polynomial Solutions Simplified

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  1. Lesson 9-2 Factoring Using the Distributive Property

  2. Definitions • Factoring - Factoring a polynomial means to find its completely factored form.

  3. Use Distributive Property - • 12a2 16a • First find the GCF of 12a2 and 16a • 12a2 = 2  2  3  a  a • 16a = 2  2  2  2  a GCF = 2  2  a = 4a Write the term as the product of the GCF and its remaining factors. Then use Distributive Property to factor out the GCF. 12a2 16a = 4a(3  a) 4a(2 2) = 4a(3a) 4a(4) = 4a(3a + 4)

  4. Use the Distributive Property to factor each polynomial • A. 15x + 25x2 • B. 12xy + 24xy2 - 30x2y4

  5. Factor by Grouping - • Factor 4ab + 8b + 3a + 6 • 4ab + 8b + 3a + 6 • (4ab + 8b) + (3a + 6) Find the GCF for both • 4b(a + 2) 3(a + 2) Factor the GCF from both groupings. • (a + 2)(4b + 3) Use FOIL method to check..

  6. Factor • 2xy + 7x - 2y -7

  7. Using the Additive Inverse Property - • Factor 35x -5xy + 3y - 21 • 35x -5xy + 3y - 21 = (35x -5xy) + (3y - 21) • = 5x(7 - y) + 3(y - 7) • = 5x(-1)(y - 7) + 3(y - 7) • = -5x(y - 7) + 3(y - 7) • = (y - 7)(-5x + 3)

  8. Factor 15a - 3ab + 4b -20

  9. Definitions • Zero Product Property - If the product of two factors is 0, then at least one of the factors must be 0. • Solve an Equation in Factored Form - • Solve (d - 5)(3d + 4) = 0 • (d - 5)(3d + 4) = 0 • = d - 5 = 0 or 3d + 4 = 0 • = d = 5 or 3d = -4 • = d = -4/3

  10. Solve (x - 2)(4x -1) = 0

  11. Solve an Equation By Factoring - • Solve x2 = 7x • x2 - 7x = 0 • = x (x-7) = 0 • = x = 0 or x - 7 = 0 • = x = 7 • The solution set is {0,7}

  12. Solve 4y = 12y2

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