You have learned how to factor the following types of ...



You have learned how to factor the following types of quadratic (2nd degree) expressions:

|Type |Example |

|GCF (Always first step!) |6x² + 15x |

| | |

|(ax² + ax) = ax(x + 1) | |

|X-box |x[pic] + 4x² - 32 |

| | |

|(x² + bx + c) or (x[pic]+bx + c) | |

|X-box & Grouping |12x² + 5x - 2 |

| | |

|(ax² + bx + c) or (ax[pic]+bx + c) | |

|DOPS |25x² - 64 |

| | |

|a² - b² = (a + b)(a – b) | |

I. Factoring Special Cubics (look for cubics with two terms ±)

SUM OF CUBES DIFFERENCE OF CUBES

a³ + b³ = a³ - b³ =

Examples: Factor each polynomial

a) 125 + x³ b) 128x[pic] - 54x

c) x³ + 8 d) 16x³ - 2

II. Factoring by Grouping (Cubics with four terms)

Examples: Factor each polynomial

a) 2x³ - x² + 2x – 1 b) 3x³ - 6x² + x – 2

c) 3x[pic] - 2x³ - 9x + 6 d) 4x³ + 16x² - x – 4

Factor the polynomials

1. x³ - 8 2. x³ + x² + x + 1

3. 10x³ + 20x² + x + 2 4. x³ + 64

5. x³ + 3x² + 10x + 30 6. 216x³ + 1

7. 125x³ - 8 8. x³ - 2x² + 4x – 8

9. 2x³ - 5x² + 18x – 45 10. -2x³ - 4x² - 3x – 6

11. 1000x[pic] + 27x 12. 27x³ + 216

13. x³ - 2x² - 9x + 18 14. 32x³ - 4

15. 2x[pic] - 54x 16. x²y² - 3x² - 4y² + 12

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