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Unit 2 – Quadratic, Polynomial, and Radical Equations and Inequalities Chapter 5 – Quadratic Functions and Inequalities 5.3 – Solving Quadratic Equations by Factoring 5.3 – Solving Quadratic Equations by Factoring In this section we will learn how to: Write quadratic equations in intercept form Solve quadratic equations by factoring 5.3 – Solving Quadratic Equations by Factoring Intercept form – of a quadratic equation is y = a(x – p)(x – q) p and q represent the x-intercepts of the graph corresponding to the equation 5.3 – Solving Quadratic Equations by Factoring Changing a quadratic in intercept form to standard forms requires using the FOIL method First Outer Inner Last Multiply the terms: first, outer, inner, last Combine any like terms 5.3 – Solving Quadratic Equations by Factoring Example 1 (6x + 1)(2x – 4) 5.3 – Solving Quadratic Equations by Factoring Example 2 (-3x + 5)(3x + 2) 5.3 – Solving Quadratic Equations by Factoring Example 3 (9x – 2)2 5.3 – Solving Quadratic Equations by Factoring Example 4 (6x + 3)2 5.3 – Solving Quadratic Equations by Factoring Example 5 (x + 7)3 5.3 – Solving Quadratic Equations by Factoring Example 6 (2x + 4)3 5.3 – Solving Quadratic Equations by Factoring Example 7 (3x – 1)3 5.3 – Solving Quadratic Equations by Factoring HOMEWORK 5.3 Part 1 Worksheet 5.3 – Solving Quadratic Equations by Factoring Find the Greatest Common Factor (GCF) If all the terms of a polynomial have a factor(s) in common, you can factor out that greatest common factor 5.3 – Solving Quadratic Equations by Factoring Example 1 Factor out the GCF 8y2 + 16y5 = 6a4 – 8a2 + 2a = -15x3y + 9x2y7 = -5x2y – x2 + 3x3y5 + 11x7 = 5.3 – Solving Quadratic Equations by Factoring CLASSWORK 5.3 Part 2 Practice 5.3 – Solving Quadratic Equations by Factoring Factoring a Difference of Perfect Squares If you have a quadratic equation that has the difference of two terms that are both perfect squares, it factors as: A2 – B2 = (A + B)(A – B) 5.3 – Solving Quadratic Equations by Factoring Example 1 Factor: x2 – 9 = 4x2 – 25 = 9x2 – 16y2 = 5.3 – Solving Quadratic Equations by Factoring Example 2 Factor: 100x2 – 81y2 = 3x2 – 75 = 20x2 – 5y2 = 5.3 – Solving Quadratic Equations by Factoring CLASSWORK/HOMEWORK 5.3 Graded Worksheet 5.3 – Solving Quadratic Equations by Factoring Factoring a Trinomial Ax2 ± Bx + C = ADD inner and outer to get B ( + )( + ) ( - )( - ) 5.3 – Solving Quadratic Equations by Factoring Example 1 Factor: x2 + 10x + 9 x2 + 8x + 15 x2 – 10x + 25 5.3 – Solving Quadratic Equations by Factoring Example 2 Factor: x2 – 2x + 1 x2 – 14x + 24 x2 + 6x + 9 5.3 – Solving Quadratic Equations by Factoring HOMEWORK 5.3 Part 3 Practice 5.3 – Solving Quadratic Equations by Factoring Factoring a Trinomial Ax2 ± Bx - C = SUBTRACT inner and outer to get B ( + )( - ) ( - )( + ) 5.3 – Solving Quadratic Equations by Factoring Example 1 Factor: x2 – 3x – 18 x2 + 5x – 6 x2 – 2x – 35 5.3 – Solving Quadratic Equations by Factoring Example 2 Factor: x2 + 4x – 21 x2 + x – 20 x2 – 4x – 5 5.3 – Solving Quadratic Equations by Factoring HOMEWORK 5.3 Part 4 Worksheet 5.3 – Solving Quadratic Equations by Factoring Factoring a Trinomial Ax2 ± Bx + C ( + )( + ) ( - )( - ) Ax2 ± Bx – C ( + )( - ) ( - )( + ) 5.3 – Solving Quadratic Equations by Factoring Example 1 Factor: 2x2 + 3x + 1 5x2 – 28x – 12 5.3 – Solving Quadratic Equations by Factoring Example 2 Factor: 4x2 – 12x + 5 3x2 + 2x – 16 5.3 – Solving Quadratic Equations by Factoring Example 3 Factor: 4x2 – 14x + 10 15x2 + 18x – 24 5.3 – Solving Quadratic Equations by Factoring Example 4 Factor: 25x2 – 10x – 3 3x2 + 11x + 6 5.3 – Solving Quadratic Equations by Factoring HOMEWORK 5.3 Part 5 Worksheet 5.3 – Solving Quadratic Equations by Factoring CLASSWORK 5.3 Graded Worksheet 5.3 – Solving Quadratic Equations by Factoring Solving by Factoring If the equation is not equal to zero, rewrite so that it is Factor out a GCF if possible You now have one of the following: A trinomial that must be factored (x2 + Bx + C) A difference of two squares that must be factored (x2 – C) Two expressions Set each of the remaining expressions equal to zero and solve 5.3 – Solving Quadratic Equations by Factoring Example 1 Factor and solve: x2 + 13x + 30 = 0 x2 + 5x – 24 = 0 5.3 – Solving Quadratic Equations by Factoring Example 2 Factor and solve: x2 – 13x = -22 x2 – 2x = 48 5.3 – Solving Quadratic Equations by Factoring Example 3 Factor and solve: x2 – 100 = 0 2x2 – 72 = 0 5.3 – Solving Quadratic Equations by Factoring Example 4 Factor and solve: x2 + 15x = 0 2x2 – 6x = 0 5.3 – Solving Quadratic Equations by Factoring HOMEWORK 5.3 Worksheet 5.3 – Solving Quadratic Equations by Factoring CLASSWORK 5.3 Graded Worksheet