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Unit 2 – Quadratic, Polynomial, and Radical Equations and Inequalities

Unit 2 – Quadratic, Polynomial, and Radical Equations and Inequalities

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Unit 2 – Quadratic, Polynomial, and Radical Equations and Inequalities

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  1. Unit 2 – Quadratic, Polynomial, and Radical Equations and Inequalities Chapter 5 – Quadratic Functions and Inequalities 5.3 – Solving Quadratic Equations by Factoring

  2. 5.3 – Solving Quadratic Equations by Factoring • In this section we will learn how to: • Write quadratic equations in intercept form • Solve quadratic equations by factoring

  3. 5.3 – Solving Quadratic Equations by Factoring • Intercept form – of a quadratic equation is • y = a(x – p)(x – q) • p and q represent the x-intercepts of the graph corresponding to the equation

  4. 5.3 – Solving Quadratic Equations by Factoring • Changing a quadratic in intercept form to standard forms requires using the FOIL method • First • Outer • Inner • Last • Multiply the terms: first, outer, inner, last • Combine any like terms

  5. 5.3 – Solving Quadratic Equations by Factoring • Example 1 • (6x + 1)(2x – 4)

  6. 5.3 – Solving Quadratic Equations by Factoring • Example 2 • (-3x + 5)(3x + 2)

  7. 5.3 – Solving Quadratic Equations by Factoring • Example 3 • (9x – 2)2

  8. 5.3 – Solving Quadratic Equations by Factoring • Example 4 • (6x + 3)2

  9. 5.3 – Solving Quadratic Equations by Factoring • Example 5 • (x + 7)3

  10. 5.3 – Solving Quadratic Equations by Factoring • Example 6 • (2x + 4)3

  11. 5.3 – Solving Quadratic Equations by Factoring • Example 7 • (3x – 1)3

  12. 5.3 – Solving Quadratic Equations by Factoring HOMEWORK 5.3 Part 1 Worksheet

  13. 5.3 – Solving Quadratic Equations by Factoring • Find the Greatest Common Factor (GCF) • If all the terms of a polynomial have a factor(s) in common, you can factor out that greatest common factor

  14. 5.3 – Solving Quadratic Equations by Factoring • Example 1 • Factor out the GCF • 8y2 + 16y5 = • 6a4 – 8a2 + 2a = • -15x3y + 9x2y7 = • -5x2y – x2 + 3x3y5 + 11x7 =

  15. 5.3 – Solving Quadratic Equations by Factoring CLASSWORK 5.3 Part 2 Practice

  16. 5.3 – Solving Quadratic Equations by Factoring • Factoring a Difference of Perfect Squares • If you have a quadratic equation that has the difference of two terms that are both perfect squares,it factors as: • A2 – B2 = (A + B)(A – B)

  17. 5.3 – Solving Quadratic Equations by Factoring • Example 1 • Factor: • x2 – 9 = • 4x2 – 25 = • 9x2 – 16y2 =

  18. 5.3 – Solving Quadratic Equations by Factoring • Example 2 • Factor: • 100x2 – 81y2 = • 3x2 – 75 = • 20x2 – 5y2 =

  19. 5.3 – Solving Quadratic Equations by Factoring CLASSWORK/HOMEWORK 5.3 Graded Worksheet

  20. 5.3 – Solving Quadratic Equations by Factoring • Factoring a Trinomial • Ax2 ± Bx+ C = • ADD inner and outer to get B • ( + ) ( + ) • ( - ) ( - )

  21. 5.3 – Solving Quadratic Equations by Factoring • Example 1 • Factor: • x2 + 10x + 9 • x2 + 8x + 15 • x2 – 10x + 25

  22. 5.3 – Solving Quadratic Equations by Factoring • Example 2 • Factor: • x2 – 2x + 1 • x2 – 14x + 24 • x2 + 6x + 9

  23. 5.3 – Solving Quadratic Equations by Factoring HOMEWORK 5.3 Part 3 Practice

  24. 5.3 – Solving Quadratic Equations by Factoring • Factoring a Trinomial • Ax2 ± Bx- C = • SUBTRACT inner and outer to get B • ( + ) ( - ) • ( - ) ( + )

  25. 5.3 – Solving Quadratic Equations by Factoring • Example 1 • Factor: • x2 – 3x – 18 • x2 + 5x – 6 • x2 – 2x – 35

  26. 5.3 – Solving Quadratic Equations by Factoring • Example 2 • Factor: • x2 + 4x – 21 • x2 + x – 20 • x2 – 4x – 5

  27. 5.3 – Solving Quadratic Equations by Factoring HOMEWORK 5.3 Part 4 Worksheet

  28. 5.3 – Solving Quadratic Equations by Factoring • Factoring a Trinomial • Ax2 ± Bx + C • ( + ) ( + ) • ( - ) ( - ) • Ax2 ± Bx – C • ( + ) ( - ) • ( - ) ( + )

  29. 5.3 – Solving Quadratic Equations by Factoring • Example 1 • Factor: • 2x2 + 3x + 1 • 5x2 – 28x – 12

  30. 5.3 – Solving Quadratic Equations by Factoring • Example 2 • Factor: • 4x2 – 12x + 5 • 3x2 + 2x – 16

  31. 5.3 – Solving Quadratic Equations by Factoring • Example 3 • Factor: • 4x2 – 14x + 10 • 15x2 + 18x – 24

  32. 5.3 – Solving Quadratic Equations by Factoring • Example 4 • Factor: • 25x2 – 10x – 3 • 3x2 + 11x + 6

  33. 5.3 – Solving Quadratic Equations by Factoring HOMEWORK 5.3 Part 5 Worksheet

  34. 5.3 – Solving Quadratic Equations by Factoring CLASSWORK 5.3 Graded Worksheet

  35. 5.3 – Solving Quadratic Equations by Factoring • Solving by Factoring • If the equation is not equal to zero, rewrite so that it is • Factor out a GCF if possible • You now have one of the following: • A trinomial that must be factored (x2 + Bx + C) • A difference of two squares that must be factored (x2 – C) • Two expressions • Set each of the remaining expressions equal to zero and solve

  36. 5.3 – Solving Quadratic Equations by Factoring • Example 1 • Factor and solve: • x2 + 13x + 30 = 0 • x2 + 5x – 24 = 0

  37. 5.3 – Solving Quadratic Equations by Factoring • Example 2 • Factor and solve: • x2 – 13x = -22 • x2 – 2x = 48

  38. 5.3 – Solving Quadratic Equations by Factoring • Example 3 • Factor and solve: • x2 – 100 = 0 • 2x2 – 72 = 0

  39. 5.3 – Solving Quadratic Equations by Factoring • Example 4 • Factor and solve: • x2 + 15x = 0 • 2x2 – 6x = 0

  40. 5.3 – Solving Quadratic Equations by Factoring HOMEWORK 5.3 Worksheet

  41. 5.3 – Solving Quadratic Equations by Factoring CLASSWORK 5.3 Graded Worksheet