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Day 139 – X-BOX Factoring.

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Presentation on theme: "Day 139 – X-BOX Factoring."— Presentation transcript:

1 Day 139 – X-BOX Factoring

2 ax2 + bx + c X- Box Trinomial (Quadratic Equation)
Product of a & c ax2 + bx + c Fill the 2 empty sides with 2 numbers that are factors of ‘a·c’ and add to give you ‘b’. b

3 x2 + 9x + 20 X- Box Trinomial (Quadratic Equation)
Fill the 2 empty sides with 2 numbers that are factors of ‘a·c’ and add to give you ‘b’. 5 4 9

4 2x2 -x - 21 X- Box Trinomial (Quadratic Equation)
-42 Fill the 2 empty sides with 2 numbers that are factors of ‘a·c’ and add to give you ‘b’. 6 -7 -1

5 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

6 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.

7 x2 -5x -10 2x Factor the x-box way Example: Factor x2 -3x -10
(1)(-10)= -10 x -5 x2 -5x x GCF -5 2 -3 2x -10 +2 GCF GCF GCF x2 -3x -10 = (x-5)(x+2)

8 First and Last Coefficients
Factor the x-box way y = ax2 + bx + c Base 1 Base 2 Product ac=mn First and Last Coefficients 1st Term Factor n GCF n m Middle Last term Factor m b=m+n Sum Height

9 Factor the x-box way Example: Factor 3x2 -13x -10 x -5 -30 3x 3x2 -15x
+2 3x2 -13x -10 = (x-5)(3x+2)

10 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)

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

12 Examples continued 2x -7 x 2x2 -7x 2x -7
3. 2x2 - 5x - 7 a) b) 2x -7 -14 -5 x 2x2 -7x 2x -7 +1 Solution: 2x2 - 5x – 7 = (2x - 7)(x + 1)

13 Examples continued 3x +2 5x 15x2 10x -3x -2
3. 15x2 + 7x - 2 a) b) 3x +2 -30 7 5x 15x2 10x -3x -1 Solution: 15x2 + 7x – 2 = (3x + 2)(5x - 1)

14 Extra Practice x2 +4x -32 4x2 +4x -3 3x2 + 11x – 20

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


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