Solving Quadratic Equations by Factoring

X- Box Product a∙c factors factors Sum b

X-box Factoring This is a guaranteed method for factoring quadratic equations—no guessing necessary! We will learn how to factor quadratic equations using the x-box method Background knowledge needed: Basic x-solve problems General form of a quadratic equation

Solve the x-box way Example: Solve 3x2 -13x -10 = 0 by factoring. x -5 (3)(-10)= -30 3x 3x2 -15x -15 2 -13 +2 2x -10 3x2 -13x -10 = 0 (x-5)(3x+2) = 0 X = 5, -2/3

First and Last Coefficients FACTOR the x-box way ax2 + bx + c GCF GCF Product ac=mn First and Last Coefficients 1st Term Factor n GCF n m Middle Last term Factor m b=m+n Sum GCF

Examples Solve using the x-box method. 1. x2 + 4x – 12 = 0 x +6 x -12 4 x 6x 6 -2 -2 -2x -12 Solution: x2 + 4x – 12 = 0 (x + 6)(x - 2) = 0 x = -6,2

Examples 2. x2 - 9x + 20 = 0 x -4 x Solution: x2 - 9x + 20 = 0 -4 -5 20 -9 x x² -4x -5 -5x 20 Solution: x2 - 9x + 20 = 0 (x - 4)(x - 5) = 0 x = 4, 5

Examples 3. 2x2 - 5x – 7 = 0 2x -7 x Solution: 2x2 - 5x – 7 = 0 -14 -5 -7 2 x -7x 2x² +1 2x -7 Solution: 2x2 - 5x – 7 = 0 (2x - 7)(x + 1) = 0 x = 7/2, -1

Examples 4. 15x2 + 7x – 2 = 0 3x +2 5x Solution: 15x2 + 7x – 2 = 0 -30 7 5x 15x² 10x 10 -3 -1 -3x -2 Solution: 15x2 + 7x – 2 = 0 (3x + 2)(5x - 1) = 0 x = -2/3, 1/5