2X-box FactoringThis is a guaranteed method for factoring quadratic equations—no guessing necessary!We will learn how to factor quadratic equations using the x-box methodBackground knowledge needed:Multiplying integersAdding & Subtracting integersGeneral form of a quadratic equation
3Standard 11.0Students 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: Use the x-box method to factor non-prime quadratic trinomials.
4Factor the x-box way Example: Factor 3x2 -13x -10 -13x x -5 3x 3x2 +23x2 -13x -10 = (x-5)(3x+2)
5Product 1st & Last (a & c) terms Factor the x-box wayy = ax2 + bx + cbxMiddle (b-term)1st Term(a-term)Product 1st & Last (a & c) termsLast term(constant)Productacx2=mn
6Factor the x-box way y = ax2 + bx + c b=m+n Sum m&n 1st Term Factor m GCFmnLast termFactornProduct of m&n (acx2)
7Examples Factor using the x-box method. 1. x2 + 4x – 12 x +6 x2 6x x a) b)x+64x-12x2x x-2xx6x-2x-2Solution: x2 + 4x – 12 = (x + 6)(x - 2)
8Examples continued 2. x2 - 9x + 20 x -4 x x2 -4x -5x 20 a) b)x-4-4x x-9x+20x2xx2 -4x-5x 20-5Solution: x2 - 9x + 20 = (x - 4)(x - 5)
9Think-Pair-ShareBased on the problems we’ve done, list the steps in the diamond/box factoring method so that someone else can do a problem using only your steps.2. Trade papers with your partner and use their steps to factor the following problem: x2 +4x -32.
10Trying out the StepsIf you cannot complete the problem using only the steps written, put an arrow on the step where you stopped. Give your partner’s paper back to him.Modify the steps you wrote to correct any incomplete or incorrect steps. Finish the problem based on your new steps and give the steps back to your partner.Try using the steps again to factor: x2 +4x -3.
11Stepping Up Edit your steps and factor: 3x2 + 11x – 20. Formalize the steps as a class.