1 / 16

Generic Rectangle Factoring

Generic Rectangle Factoring. Diamond Problem. Product. 3. -9. Sum. Warm-Up. Please complete these individually. 1. Fill in the following Diamond problems. a. b. c. 2. Write the general form of a quadratic equation.

naoko
Download Presentation

Generic Rectangle Factoring

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Generic Rectangle Factoring

  2. Diamond Problem Product 3 -9 Sum

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

  4. Generic Rectangle • This is a guaranteed method for factoring quadratic equations—no guessing necessary! • We will learn how to factor quadratic equations using the diamond/generic rectangle method • Background knowledge needed: • Basic diamond problems • General form of a quadratic equation

  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 diamond/generic rectangle method to factor non-prime trinomials.

  6. Diamond/generic rectangle method of factoring Example: Factor 3x2 -13x -10 (3)(-10)= -30 x -5 3x 3x2 -15x 2 -15 -13 -10 2x +2 3x2 -13x -10 = (x-5)(3x+2)

  7. Diamond/generic rectangle 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

  8. -12 4 Examples Factor using the diamond/generic rectangle. 1. x2 + 4x – 12 a) b) x +6 x26x -2x -12 x 6 -2 -2 Solution: x2 + 4x – 12 = (x + 6)(x - 2)

  9. Examples continued 2. x2 - 9x + 20 a) b) x -4 -4-5 20 -9 x2-4x -5x 20 x -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 -72 -14 -5 x 2x2-7x 2x -7 +1 Solution: 2x2 - 5x – 7 = (2x - 7)(x + 1)

  14. Examples continued 3. 15x2 + 7x - 2 a) b) 3x +2 -30 7 5x 15x210x -3x -2 10-3 -1 Solution: 15x2 + 7x – 2 = (3x + 2)(5x - 1)

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

  16. Independent Practice Do the worksheets for Homework using the diamond/generic rectangle method. Show all your work to receive credit– don’t forget to check by multiplying!

More Related