What you will learn A review of all kinds of factoring (yippee) How to solve a quadratic by factoring The zero product property

Solving Quadratic Equations by Factoring Vocabulary: Monomial: An expression that has only one term. e.g. 2x Binomial: An expression with two terms e.g.: x + 5 Trinomial: An expression with three terms e.g.: x2 + 2x + 3 Factoring: Writing a trinomial as a product of binomials (un “foiling”). Objective: 5.2 Solving Quadratic Equations by Factoring

Examples Factor x2 – 12x – 28 This puts the quadratic equation in intercept form. Objective: 5.2 Solving Quadratic Equations by Factoring

You Try Factor x2 – 2x - 48 Objective: 5.2 Solving Quadratic Equations by Factoring

When “A” is not 1 Factor 3x2 – 17x + 10 Objective: 5.2 Solving Quadratic Equations by Factoring

You Try Factor 4y2 – 4y - 3 Objective: 5.2 Solving Quadratic Equations by Factoring

Special Factoring Patterns Pattern name Pattern Example Diff of Squares a2 – b2 = (a + b)(a – b) x2 – 9 (x + 3)(x – 3) Perfect Sq. Trinomial a2 + 2ab + b2 x2 + 12x + 36 (a + b)2 (x + 6)2 a2 – 2ab + b2 x2 – 8x + 16 (a – b)2 (x – 4)2 Objective: 5.2 Solving Quadratic Equations by Factoring

Factoring with Special Patterns - Examples Difference of squares: 4x2 – 25 Perfect square trinomial: 9y2 + 24y + 16 Perfect square trinomial: 49r2 – 14r + 1 Objective: 5.2 Solving Quadratic Equations by Factoring

You Try Factor the following: 1. x2 – 25 2. 4x2 + 12x + 9 Objective: 5.2 Solving Quadratic Equations by Factoring

Factoring Monomials First Factor the following: 1. 5x2 – 20 2. 6p2 + 15p + 9 3. 2u2 + 8u Objective: 5.2 Solving Quadratic Equations by Factoring

You Try Factor the following: 1. 14x2 + 2x – 12 2. 3v2 – 18v Objective: 5.2 Solving Quadratic Equations by Factoring

Finally…we are going to solve these things Zero Product Property: Let A and B be real numbers or algebraic expressions. If AB = 0 then A = 0 or B = 0. Examples: (x – 3)(x + 4) = 0 then either x – 3 equals zero of x + 4 equals zero. Objective: 5.2 Solving Quadratic Equations by Factoring

Solving Quadratic Equations Solve: 1. x2 + 3x – 18 = 0 2. 2t2 – 17t + 45 = 3t - 5 Objective: 5.2 Solving Quadratic Equations by Factoring

You Try Solve. 1. 9t2 – 12t + 4 = 0 2. 3x – 6 = x2 - 10 Objective: 5.2 Solving Quadratic Equations by Factoring

A Word Problem You have made a rectangular stained glass window that is 2 feet by 4 feet. You have 7 square feet of clear glass to create a border of uniform width around the window. What should the width of the border be? Area of border = area of border and wind. – area of wind. Objective: 5.2 Solving Quadratic Equations by Factoring

Finding “Zeros” of Quadratic Functions Two Ways: 1. Factoring! y = x2 – x – 6 2. Calculator! Objective: 5.2 Solving Quadratic Equations by Factoring

Homework page 260, 24-30 even, 36, 38, 47, 48-58 even, 66-76 even, 80-84 even Objective: 5.2 Solving Quadratic Equations by Factoring