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Mastering Polynomial Factoring: Cubic Equations Guide

Learn how to factor cubic equations effortlessly using the sum and difference of cubes formulas. Practice problems included for better understanding. Improve your algebra skills today!

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Mastering Polynomial Factoring: Cubic Equations Guide

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  1. Warm-Up Factor. x2 – 10x + 25 64x2 – 16x + 1 Multiply. 3. (5x + 3y)(5x + 3y) Homework: HW P5B (57-64 all) Answers: (x-5)2 (8x-1)2 25x2 +30xy +9y2

  2. Answers to HW P5A #17-37 odds, 49-55 odds 17. (x+2)(x+3) 19. (x-5)(x+3) 21. (x-5)(x-3) 23. (3x+2)(x-1) 25. (3x-28)(x+1) 27. (2x-1)(3x-4) 29. (2x+3)(2x+5) 31. (3x-1)(3x-2) 33. (5x+8)(4x-1) 35. (2x+y)(x+y) 37. (3x+2y)(2x-3y) 49. (x+1)2 51. (x-7) 2 53. (2x+1) 2 55. (3x-1) 2

  3. Objective:Factoring Polynomials • Factoring the Sum and Difference of Cubes:

  4. P5B-- Factoring Continued: Factoring the Sum and Difference of Cubes: Don’t forget to check for the GCF!! Formulas: SUM: A3 + B3 = (A+B)(A2 – AB + B2) DIFFERENCE: A3 - B3 = (A-B)(A2 + AB + B2) A and B come from cube rooting the terms in the problem.

  5. Example 1: x3 + 8 Step 1: Check for GCF, there is none Step 2: Cube root each of the terms A = x and B = 2 Step 3: Follow formula A3 + B3 = (A+B)(A2 – AB + B2) = (x+ 2)(x2 - 2x + 4)

  6. Example 2 Continued: b) 64x3 -125 Step 1: Check for GCF, there is none Step 2: Cube root terms A = 4x and B = 5 Step 3: Follow formula A3 - B3 = (A-B)(A2 + AB + B2) = (4x-5)(16x2 + 20x + 25)

  7. YOU TRY!!! x3 + 64 b) 125x3 – 8 Answers: (x+4)(x2 – 4x + 16) (5x – 2)(25x2 + 10x + 4)

  8. In your Reflection Notebook: Explain in writing how to factor a cubic equation. x3+1 Tonight’s homework: HW P5B, #57-64 all

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