Generic rectangle factoring
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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.

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Generic Rectangle Factoring

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Generic rectangle factoring

Generic Rectangle Factoring


Diamond problem

Diamond Problem

Product

3

-9

Sum


Warm up

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


Generic rectangle

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


Standard 11 0

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.


Diamond generic rectangle method of factoring

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)


Diamond generic rectangle

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


Examples

-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)


Examples continued

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)


Think pair share

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.


Trying out the steps

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.


Stepping up

Stepping Up

  • Edit your steps and factor: 3x2 + 11x – 20.

  • Formalize the steps as a class.


Examples continued1

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)


Examples continued2

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)


Guided practice

Guided Practice

Grab your white boards, pens and erasers!


Independent practice

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!


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