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Published byWarren Stanley Modified over 8 years ago

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Warm-up Find the quotient. 1. 2. 3.

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Section 6-4: Solving Polynomial Equations by Factoring Goal 1.03: Operate with algebraic expressions (polynomial, rational, complex fractions) to solve problems.

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Sum of Cubes a 3 + b 3 = (a + b)(a 2 – ab + b 2 ) ex1: Factor x 3 + 8 x 3 + 8 = (x) 3 + (2) 3 = (x + 2)(x 2 – 2x + 4) ex2: Solve 27x 3 + 1 = 0 27x 3 + 1 = (3x) 3 + (1) 3 = (3x + 1)(9x 2 – 3x + 1)

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Difference of Cubes a 3 - b 3 = (a - b)(a 2 + ab + b 2 ) ex1: Factor x 3 – 125 x 3 – 125 = (x) 3 – (5) 3 = (x – 5)(x 2 + 5x + 25) ex2: Solve 8x 3 – 1 = 0 8x 3 – 1 = (2x) 3 – (1) 3 = (2x – 1)(4x 2 + 2x + 1)

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Factoring using a Quadratic Form ex1: Factor x 4 – 2x 2 – 8 (x 2 + 2)(x 2 – 4) (x 2 + 2)(x + 2)(x – 2) ex2: Factor x 4 + 7x 2 + 6 (x 2 + 6)(x 2 + 1) ex3: Factor x 4 – 3x 2 – 10 (x 2 – 5)(x 2 + 2)

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ex4: Factor x 4 – 1 (x 2 + 1)(x 2 – 1) (x 2 + 1)(x + 1)(x – 1) ex5: Factor x 4 – 6x 2 – 27 (x 2 + 3)(x 2 – 9) (x 2 + 3)(x + 3)(x – 3)

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Solve by Graphing

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Classwork/ Homework Classwork: #1, 11, 13, 19, 21, 27 Homework: #6, 10, 14, 20, 26, 30

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