X-box Factoring X- Box Trinomial (Quadratic Equation) ax2 + bx + c Fill the 2 empty sides with 2 numbers that are factors of ‘a·c’ and add to give you ‘b’. Product of a & c b X- Box Trinomial (Quadratic Equation) x2 + 9x + 20 Fill the 2 empty sides with 2 numbers that are factors of ‘a·c’ and add to give you ‘b’. 20 5 4 9 X- Box Trinomial (Quadratic Equation) 2x2 -x - 21 Fill the 2 empty sides with 2 numbers that are factors of ‘a·c’ and add to give you ‘b’. -42 -7 6 -1 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 LET’S TRY IT! Students apply basic factoring techniques to secondand 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. Factor the x-box way Example: Factor x2 -3x -10 (1)(-10)= x -10 -5 -5 x x2 -5x GCF +2 2x -10 GCF GCF GCF 2 -3 x2 -3x -10 = (x-5)(x+2) Factor the x-box way y = ax2 + bx + c First and Last Coefficients Product Base 1 Base 2 ac=mn GCF 1st Term Factor n Height Factor m Last term n m b=m+n Sum Middle Factor the x-box way Example: Factor 3x2 -13x -10 x -5 3x 3x2 -15x +2 2x -10 -30 2 -15 -13 3x2 -13x -10 = (x-5)(3x+2) Examples Factor using the x-box method. 1. x2 + 4x – 12 a) x b) 6 -12 4 -2 +6 x x2 6x -2 -2x -12 Solution: x2 + 4x – 12 = (x + 6)(x - 2) Examples continued 2. x2 - 9x + 20 a) 20 -4 -5 -9 x b) x x2 -4 -4x -5 -5x 20 Solution: x2 - 9x + 20 = (x - 4)(x - 5) Examples continued 3. 2x2 - 5x - 7 a) b) -14 -7 -5 2x 2 x +1 -7 2x2 -7x 2x -7 Solution: 2x2 - 5x – 7 = (2x - 7)(x + 1) Examples continued 3. 15x2 + 7x - 2 a) -30 10 -3 7 b) 3x +2 5x 15x2 10x -1 -3x -2 Solution: 15x2 + 7x – 2 = (3x + 2)(5x - 1) Extra Practice 1. x2 +4x -32 2. 4x2 +4x -3 3. 3x2 + 11x – 20 Reminder!! Don’t forget to check your answer by multiplying!

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# Factoring Quadratics with a box