The document explains and provides examples of how to factor quadratic expressions using the "x-box" method. This method involves drawing an x-box with the coefficients of the expression and identifying the greatest common factor and two binomial factors that multiply to the original expression. Three examples are provided and worked through step-by-step to demonstrate how to set up and solve factoring problems using the x-box method.

1. X-box Factoring

2. X- Box 3 -9 Product Sum

3. Factor the x-box way Middle b= m + n Sum Product a c = m n m n First and Last Coefficients y = ax 2 + bx + c Last term 1st Term Factor n Factor m Base 1 Base 2 GCF Height

4. Examples Factor using the x-box method. 1. x 2 + 4x – 12 a) b) x 6 -2 x 2 6 x -2 x -12 x -2 +6 Solution: x 2 + 4x – 12 = (x + 6 )(x - 2 ) -12 4

5. Examples continued 2. x 2 - 9x + 20 a) b) 20 -9 x 2 -4 x -5 x 20 x x -4 -5 Solution: x 2 - 9x + 20 = (x - 4 )(x - 5 ) -4 -5

6. Examples continued 3. 2x 2 - 5x - 7 a) b) -14 -5 2x 2 -7 x 2 x -7 x 2x -7 +1 Solution: 2x 2 - 5x – 7 = (2x - 7 )(x + 1 ) -7 2

7. Examples continued 3. 15x 2 + 7x - 2 a) b) -30 7 15x 2 10 x -3 x -2 5x 3x +2 -1 Solution: 15x 2 + 7x – 2 = (3x + 2 )(5x - 1 ) 10 -3