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X-box Factoring

Learn how to factor quadratic equations using the X-Box method. Apply basic factoring techniques to solve polynomials efficiently. Practice with examples and guided steps!

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X-box Factoring

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  1. X-box Factoring

  2. X- Box Product 3 -9 Sum

  3. Warm-Up Please complete these individually. 1. Fill in the following X-solve problems. a. b. c. 2. Write the general form of a quadratic equation. 3. Divide using the box method. a. 4a3 + 12a2 + 6a b. 14x5y3 – 35x4y2 + 21x2y 2a 7xy

  4. 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 • Background knowledge needed: • Basic x-solve problems • General form of a quadratic equation • Dividing a polynomial by a monomial using the box method

  5. Standard 11.0 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.

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

  7. Factor the x-box way y = ax2 + bx + c Base 1 Base 2 Product ac=mn First and Last Terms Quadratic Term Factor n GCF n m Constant term Factor m b=m+n Sum Height Middle Term

  8. (8x2)(-3) =-24x2 -2x Examples Factor using the x-box method. 1. 8x2 - 2x – 3 a) b) -3 4x 8x2-6x +4x-3 2x -6x +4x +1 Solution: 8x2 - 2x – 3 = (4x - 3)(2x + 1)

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

  10. Think-Pair-Share • Based on the problems we’ve done, list the steps in the diamond/box factoring method so that someone else can do a problem using only your steps. 2. Trade papers with your partner and use their steps to factor the following problem: x2 + 4x -32.

  11. Trying out the Steps • If you cannot complete the problem using only the steps written, put an arrow on the step where you stopped. Give your partner’s paper back to him. • Modify the steps you wrote to correct any incomplete or incorrect steps. Finish the problem based on your new steps and give the steps back to your partner. • Try using the steps again to factor: 4x2 + 4x -3.

  12. Stepping Up • Edit your steps and factor: 3x2 + 11x – 20. • Formalize the steps as a class.

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

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

  15. -36 0 Examples Factor using the x-box method. 4. 9x2+ 0x – 4 a) b) 3x +2 9x2 +6x -6x -4 3x 6 -6 -2 Solution: 9x2 – 4 = (3x + 2)(3x - 2)

  16. Guided Practice Grab your white boards, pens and erasers!

  17. Independent Practice Do the worksheets for Homework using the x-box method. Show all your work to receive credit– don’t forget to check by multiplying!

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