Xbox Factoring X Box Trinomial Quadratic Equation ax

X-box Factoring

X- Box Trinomial (Quadratic Equation) ax 2 + 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) x 2 + 9 x + 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) 2 x 2 -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 x 2 -3 x -10 (1)(-10)= x -10 -5 -5 x x 2 -5 x GCF +2 2 x -10 GCF GCF 2 -3 x 2 -3 x -10 = (x-5)(x+2)

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

Factor the x-box way Example: Factor 3 x 2 -13 x -10 x -5 3 x 3 x 2 -15 x +2 2 x -10 -30 2 -15 -13 3 x 2 -13 x -10 = (x-5)(3 x+2)

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

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

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

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

Extra Practice 1. x 2 +4 x -32 2. 4 x 2 +4 x -3 3. 3 x 2 + 11 x – 20

Reminder!! Don’t forget to check your answer by multiplying!