Factoring Quadratics

Special Factoring Patterns Difference of Squares a2 – b2 = (a + b)(a – b) Example: x2 – 36 = (x + 6)(x – 6) a2 – 49 = (x + 7)(x – 7)

Special Factoring Patterns Perfect Square Trinomial a2 + 2ab + b2 = (a + b)2 a2 - 2ab + b2 = (a - b)2 Example: a2 + 8a + 16 = (a + 4)2 a2 – 10a + 25 = (a - 5)2

X-box Factoring

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 Dividing a polynomial by a monomial using the box method

Standard 11.0 Students apply basic factoring techniques to second- and simple third-degree polynomials. These techniques include finding a common factor for all terms in a polynomial, recognizing the difference of two squares, and recognizing perfect squares of binomials. Objective: I can use the x-box method to factor non-prime trinomials.

First and Last Coefficients Factor the x-box way y = 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 Factor using the x-box method. 1. x2 + 4x – 12 x +6 x2 6x x a) b) x +6 -12 4 x2 6x -2x -12 x 6 -2 -2 Solution: x2 + 4x – 12 = (x + 6)(x - 2)

Examples continued 2. x2 - 9x + 20 x -4 x x2 -4x -5x 20 a) b) x -4 -4 -5 20 -9 x x2 -4x -5x 20 -5 Solution: x2 - 9x + 20 = (x - 4)(x - 5)

Guided Practice Grab your worksheets, pens and erasers!

Practice Factor: x2 – 7x +10 (x -5)(x – 2) q2 – 11q +28 (q - 7)(q – 4)

Practice Factor: x2 – 81 (x - 9)(x + 9) q2 – 26q +169 (q - 13)2

Practice Factor: x2 – 49 (x - 7)(x + 7) q2 – 16q + 64 (q - 8)2