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5.3 Factoring and Solving Quadratics (work).notebook October 18, 2016 5.3 FACTORING QUADRATICS There are several methods available for solving a quadratic equation: 1. 2. 3. 4. 5. By Square Roots By Factoring By Completing the Square By the Quadratic Formula By Graphing The method depends on the form of the equation. FACTORING QUADRATIC TRINOMIALS Example: 5x2 + 17x + 14 1. The expression must be in ascending or descending order. 2. Make a sum/product chart. 3. Divide each number by the leading coefficient. 4. Reduce each fraction if possible . 5. Denominator = constant or coefficient of first term Numerator = constant or coefficient of last term 5.3 Factoring and Solving Quadratics (work).notebook October 18, 2016 Examples: a. x2 + 6x + 8 b. 3x2 - 11x + 6 Examples: c. x2 + 7x - 18 d. 3x2 +10x - 8 5.3 Factoring and Solving Quadratics (work).notebook October 18, 2016 Practice Factor each trinomial. 1) x2 - 16x + 39 2) x2 + 2x - 35 3) x2 + 22x + 121 4) x2 - 2x - 63 5) 14x2 - 11x + 2 6) 12x2 + 16x - 3 7) 2x2 + 13x + 6 8) 9x2 - 9x - 28 Answers Factor each trinomial. 1) x2 - 16x + 39 (x - 3)(x - 13) 2) x2 + 2x - 35 (x + 7)(x - 5) 3) x2 + 22x + 121 (x + 11)(x + 11) 4) x2 - 2x - 63 (x + 7)(x - 9) 5) 14x2 - 11x + 2 (7x - 2)(2x - 1) 6) 12x2 + 16x - 3 (2x + 3)(6x - 1) 7) 2x2 + 13x + 6 (2x + 1)(x + 6) 8) 9x2 - 9x - 28 (3x + 4)(3x - 7) 5.3 Factoring and Solving Quadratics (work).notebook October 18, 2016 Special Factoring Patterns 1. FACTORING DIFFERENCE OF SQUARES x2 4 = (x 2)(x + 2) W 4x 9 = (2x 3)(2x + 3) 2 ha t is th e x 49 = (x 7)(x + 7) 2 pa tt er 64x2 25 = (8x 5)(8x + 5) n? a2 b2 = Special Factoring Patterns 2. PERFECT SQUARE TRINOMIALS x2 + 14x + 49 = (x + 7)2 W x2 8x + 16 = (x 4)2 4x2 20x + 25 = (2x 5)2 9x2 + 12x + 4 = (3x + 2)2 a2 2ab + b2 = a2 + 2ab + b2 = ha t is th e pa tt er n ? 5.3 Factoring and Solving Quadratics (work).notebook October 18, 2016 Practice Factor completely. 1. 4x 2 - 121 2. 9x 2 - 24x + 16 3. 225 - x 2 4. x 2 + 10x + 25 5. 10x 2 - 13x - 3 Answers Factor completely. 1. 4x2 - 121 2. 9x 2 - 24x + 16 (2x - 11)(2x + 11) (3x - 4) 2 3. 225 - x 2 (15 - x)(15 + x) 5. 10x2 - 13x - 3 (2x - 3)(5x + 1) 4. x 2 + 10x + 25 (x + 5)2 5.3 Factoring and Solving Quadratics (work).notebook October 18, 2016 When factoring, ALWAYS look for the GCF first! Greatest Common Factor the largest factor that divides ALL of the terms a. 12x2 - 3 b. 7v2 - 42v FACTOR COMPLETELY d. 15x2 + 6x c. 5x2 - 45 e. 3x 2 - 9x + 6 f. 36x - 48x 2 + 24x3