ax 2 + bx + c Product of a & c Fill the 2 empty sides with 2 - PowerPoint PPT Presentation

D AY 139 – X-BOX F ACTORING

X- B OX Trinomial (Quadratic Equation) ax 2 + bx + c Product of a & c Fill the 2 empty sides with 2 numbers that are factors of ‘a·c’ and add to b give you ‘b’.

X- B OX Trinomial (Quadratic Equation) x 2 + 9x + 20 20 5 Fill the 2 empty sides 4 with 2 numbers that are factors of ‘a·c’ and add to 9 give you ‘b’.

X- B OX Trinomial (Quadratic Equation) 2x 2 -x - 21 -42 Fill the 2 empty sides -7 6 with 2 numbers that are factors of ‘a·c’ and add to -1 give you ‘b’.

X- BOX F ACTORING  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 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.

F ACTOR THE X - BOX WAY Example: Factor x 2 -3x -10 (1)(-10)= x -5 -10 x 2 -5x x GCF -5 2 -3 -10 2x +2 GCF GCF GCF x 2 -3x -10 = (x-5)(x+2)

F ACTOR THE X - BOX WAY y = ax 2 + bx + c Base 1 Base 2 Product First and ac=mn 1st Last Factor GCF Term Coefficients n n m Middle Last Factor b=m+n Height term m Sum

F ACTOR THE X - BOX WAY Example: Factor 3x 2 -13x -10 x -5 -30 3x 3x 2 -15x 2 -15 -13 -10 2x +2 3x 2 -13x -10 = (x-5)(3x+2)

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

E XAMPLES CONTINUED 2. x 2 - 9x + 20 x -4 a) b) 20 x 2 -4x x -4 -5 -5x 20 -5 -9 Solution: x 2 - 9x + 20 = (x - 4)(x - 5 )

E XAMPLES CONTINUED 3. 2x 2 - 5x - 7 2x -7 a) b) -14 2x 2 -7x x -7 2 -5 +1 2x -7 Solution: 2x 2 - 5x – 7 = (2x - 7)(x + 1 )

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

E XTRA P RACTICE x 2 +4x -32 1. 4x 2 +4x -3 2. 3x 2 + 11x – 20 3.

R EMINDER !! Don’t forget to check your answer by multiplying!