# Diamond and Box Factoring - Ms. Billerbeck's Site

X-box Factoring Warm-Up Please complete these individually. 1. Fill in the following X-solve problems. a. b. 4 7 c.

15 36 10 13 2. Write the general form of a quadratic equation. 3. Divide using the box method. a. 4a3 + 12a2 + 6a 2a b. 14x5y3 35x4y2 + 21x2y 7xy

X- Box Product 3 -9 Sum X-box Factoring This is a guaranteed method for factoring quadratic equationsno 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 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. Factor the x-box way Example: Factor 3x2 -13x -10 (3)(-10)=

-30 2 -15 x -5 3x 3x2 -15x +2

2x -10 -13 3x2 -13x -10 = (x-5)(3x+2) Factor the x-box way y = ax2 + bx + c First and Last Coefficients Produ ct GCF

ac=mn n m Middle b=m+ Height n Sum Base 1 Base 2 1st Term

Factor n Factor m Last term Examples Factor using the x-box method. 1. x2 + 4x 12 a) b) x

-12 6 -2 4 x -2 x 2 + 6x 6

-2x -12 Solution: x2 + 4x 12 = (x + 6)(x - 2) Examples continued 2. x2 - 9x + 20 a) 20 -4 -5 -9 b)

x x -4 x2 -4x -5 -5x 20 Solution: x2 - 9x + 20 = (x - 4)(x - 5) Think-Pair-Share 1. Based on the problems weve 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. Trying out the Steps 3. If you cannot complete the problem using only the steps written, put an arrow on the step where you stopped. Give your partners paper back to him. 4. 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. 5. Try using the steps again to factor: 4x2 +4x -3. Stepping Up 6. Edit your steps and factor:

3x2 + 11x 20. 7. Formalize the steps as a class. Examples continued continued 3. 2x2 - 5x - 7 a) -14 -7 2 -5 2x b) x

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

7 b) 3x + 2 2 5x 15x 10x -1 -3x -2 Solution: 15x2 + 7x 2 = (3x + 2)(5x - 1) Guided Practice

Grab your white boards, pens and erasers! Independent Practice Do the worksheets for Homework using the x-box method. Show all your work to receive credit dont forget to check by multiplying!

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