Mastering Quadratic Equations with the X-Box Factoring Method

Dive into the world of factoring quadratic equations using the X-Box method. This reliable approach eliminates the guesswork and guides you through efficiently factoring trinomials. Learn how to find the factors of ac, determine the missing terms, and simplify complex expressions. Explore examples and step-by-step explanations to enhance your skills in factoring non-prime trinomials effortlessly.

• Quadratic Equations
• X-Box Factoring
• Factoring Techniques
• Mathematics Education
• Trinomials

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1. X-box Factoring

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

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

4. X- Box Trinomial (Quadratic Equation) 2x2 -x - 21 -42 Fill the 2 empty sides with 2 numbers that are factors of a c and add to give you b . -7 6 -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. LETS 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. Factor the x-box way Example: Factor x2 -3x -10 (1)(-10)= -10 x -5 x2 -5x x GCF -5 2 -3 -10 2x +2 GCF GCF GCF x2 -3x -10 = (x-5)(x+2)

8. 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 -15 -13 -10 2x +2 3x2 -13x -10 = (x-5)(3x+2)

10. Examples Factor using the x-box method. 1. x2 + 4x 12 x +6 a) b) -12 x2 6x x 6 -2 4 -2 -2x -12 Solution: x2 + 4x 12 = (x + 6)(x - 2)

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

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

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

14. Extra Practice 1. x2 +4x -32 2. 4x2 +4x -3 3. 3x2 + 11x 20

15. Reminder!! Don t forget to check your answer by multiplying!