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Warm - up 6.4 Factor: 1. 4x 2 – 24x4x(x – 6) 2. 2x x – 21 (2x – 3)(x + 7) 3. 4x 2 – 36x + 81 (2x – 9) 2 Solve: 4. x x + 25 = 0x = x 2 + x = 15x = 3 / 2 and - 5 / 3

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6.4 solving polynomial equations by Jason L. Bradbury CA State Standard Students are adept at operations on polynomials, including long division Students factor polynomials representing the difference of squares, perfect square trinomials, and the sum and difference of two cubes. Objective – To be able to factor and solve polynomial expressions.

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2x 2 – 5x – 12 In Ch. 5 we learned how to factor: - A General Trinomial 6.4 solving polynomial equations (2x + 3)(x – 4) - A Perfect Square Trinomial x x + 25 (x + 5)(x + 5) = (x +5) 2 - The Difference of two Squares 4x 2 – 9 (2x) 2 – 3 2 (2x + 3)(2x – 3) - A Common Monomial Factor 6x x 3x(2x + 5)

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a) x 4 – 6x 2 – 27 Example 1 Factor (x 2 + ?)(x 2 – ?) (x 2 + 3)(x 2 – 9) (x 2 + 3)(x – 3)(x + 3) b) x 4 – 3x 2 – 10 (x 2 + ?)(x 2 – ?) (x 2 + 2)(x 2 – 5)

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a 3 + b 3 = (a + b)(a 2 - ab + b 2 ) Sum of Two Cubes ** Special Factoring Patterns ex. x a = x (x + 2)(x 2 – 2x + 4) a 3 – b 3 = (a – b)(a 2 + ab + b 2 ) Example 2 x x Difference of Two Cubes b = 2 ex. 8x 3 – 1 x a = 2x (2x – 1)(4x 2 + 2x + 1) b = 1 (2x) 3 – (1) 3 = (x + 5)(x 2 – 5x + 25)

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a) x 3 – 27 Example 3 Factor a 3 – b 3 = (a – b)(a 2 + ab + b 2 ) x 3 – 3 3 = (x – 3)(x 2 + 3x + 9) b) 8x a 3 + b 3 = (a + b)(a 2 - ab + b 2 ) (2x) 3 + (4) 3 = (2x + 4)(4x 2 – 8x + 16)

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Must be the same x 2 (x – 2) x 3 – 2x 2 – 9x + 18 (x 2 – 9)(x – 2) Extra Example 2 Factor by grouping -9(x – 2) (x – 3)(x + 3)(x – 2)

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6.4 Homework Page 336 – – 14, 21 – 27, and 31

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6.4 Guided Practice Page 336 – – 14 and 21 – 24

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