Setting up the Area Model of Factoring a quadratic

Factoring Trinomials when A = 1

• When factoring polynomials, we are "undoing" the multiplication of two binomials.

• Remember: Factoring is the process of finding the factors that would multiply together to make a certain polynomial. 

​We have learned this...

​(x + 2)(x + 3) = x² + 5x + 6

​We are going to learn this.

​x² + 5x + 6 = (x + 2)(x + 3)

​Remember:

​ALWAYS look for a GCF first!

​

GCF: Greatest Common Factor

​

​If you can divide a common factor out, it makes the rest of the problem much easier to do!

Multiple Choice

What is the GCF of 18 and 45?

• 3

• 12

• 9

• 6

Multiple Choice

What is the GCF of the trinomial? 3x³ - 9x -120x²

• 3x

• 27

• 3

• none

Multiple Choice

Factor out the GCF of 10x + 50

• 10(10x+50)
• 10(x+50)
• 10(x+5)
• Cannot be factored

Multiple Choice

Fill in the missing numbers. (order doesn't matter)

• 1,3

• -1, -3

• 3, 12

• -1, 12

Multiple Choice

Fill in the missing numbers. (order doesn't matter)

• -3, -1
• 1,3
• 0, 1
• 1,-12

Multiple Choice

Fill in the missing numbers. (order doesn't matter)

• 2,7
• -2,7
• -7,-2
• 2,5

​Setting up Diamond Problem

​a = 2
b = -5
c = 3

​2 x 3


6

​-5

​You are trying to find two numbers that multiply to 6 and add to -5

​Once you've found the GCF...

Factor it out! Then what's left goes in our diamond problem and into our area model box!

4.10B - Factoring Polynomials

Factoring when a>1

1. Look for the GCF First!​

2. Find what multiplies to a⋅c and adds to b?

The Box Method/Area Model

• Place the first term in the first inside box (top left) and the last term in the last box (bottom right)

• Find the factors of axc that add to b (diamond problem).

• Place those factors with x's in the other two boxes. It doesn't matter which is which.

• Factor out the GCF in each row and each column.

• Now group the outside and you're done!

Multiple Choice

Find the expression that should replace D

• -5

• 5x

• -x

• -1

Multiple Choice

When using the box method to solve $$x^2-6x+8$$ , which of the following is correct?

Multiple Choice

When solving $$9x^2-4$$ , which of the following is the correct set up when using the box method?

Multiple Choice

What is the first step in factoring $$6x^2+14x-12$$  ?

• Multply a and c to get -36

• Factor out a GCF of 2

• Put the first term in the first box and last term in the last box

• Find the factors that multiply to -36 and add to 14

Multiple Choice

Identify the error:

• found the wrong factors of ac (-18)

• factors did not add to b (7)

• first term and last term entered incorrectly in the box

• Factored out the GCF in each column and row incorrectly

Multiple Choice

Using the box method, which is the correct way to solve $$4x^2+9x+2$$  

Multiple Choice

Which is the correct set up for factoring $$10x^2+7x+1$$ using the box method? 

​Please go to your packet from last class. You will be continuing to work on it. It is due next class. Please refer to this quizizz if you need help remembering how to set up the box.

It is linked on your canvas homepage.