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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 ax bx c 0 2 Solve the x-box way Example: Factor 3x2 -13x -10 = 0 x -5 3x 3x2 -15x +2 2x -10 (3)(-10)= -30 2 -15 -13 3x2 -13x -10 = 0 (x-5)(3x+2) = 0 X = 5, -2/3 FACTOR the x-box way ax2 + bx + c First and Last Coefficients Product GCF GCF ac=mn GCF 1st Term Factor n GCF Factor m Last term n m b=m+n Sum Middle Examples Solve using the x-box method. 1. x2 + 4x – 12 = 0 6 -12 4 -2 x +6 x x2 6x -2 -2x -12 Solution: x2 + 4x – 12 = 0 (x + 6)(x - 2) = 0 x = -6,2 Examples 2. x2 - 9x + 20 = 0 20 -4 -5 -9 x -4 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 -14 -7 2 -5 2x x +1 2x² 2x Solution: 2x2 - 5x – 7 = 0 (2x - 7)(x + 1) = 0 x = 7/2, -1 -7 -7x -7 Examples 4. 15x2 + 7x – 2 = 0 -30 10 -3 7 5x -1 3x +2 15x² 10x -3x -2 Solution: 15x2 + 7x – 2 = 0 (3x + 2)(5x - 1) = 0 x = -2/3, 1/5