Factoring Polynomials, Special Cases

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Presentation transcript:

Factoring Polynomials, Special Cases The Difference of Two Squares: a2 – b2 = (a + b)(a – b) 9x2 – 16 x4 – 81 3. 32 – 2x6 (3x + 4)(3x – 4) (x2 + 9)(x2 – 9) 2 (4 + x3)(4 – x3)

Factoring Polynomials, Special Cases The Difference of Two Cubes: a3 – b3 = (a – b)(a2 + ab + b2) (The trinomial cannot be factored any further.) 27x3 – 125 24 – 3x3 X6 – 343 (3x – 5)(9x2 + 15x + 25) 3 (2 – x)(4 + 2x + x2) (x2 – 7)(x4 + 7x2 + 49)

Factoring Polynomials, Special Cases The Sum of Two Cubes: a3 + b3 = (a + b)(a2 – ab + b2) (The trinomial cannot be factored any further.) x3 + 8 1000x9 + 1 162 + 750x3 1. (x + 2)(x2 – 2x + 4) 2. (10x3 + 1)(100x6 – 10x3 + 1) 3. 6 (3 + 5x) (9 – 15x + 25x2)

Factoring Polynomials, Special Cases The Four Term Grouping Method 1. x3 – 2x2 – 9x + 18 2. 6x + 14x3 – 35x2 – 15 3. x3 + 6x2 – 4x – 24 4. 4x4 + 12x3 – 4x2 – 12x 1. (x + 3)(x – 3)(x – 2) 2. (2x – 5)(7x2 + 3) 3. (x + 2)(x – 2)(x + 6) 4. 4x (x + 1)(x – 1)(x + 3)