Diamond Factoring

Factoring Review

Learning Target: I can factor quadratic expressions

Poll

Do you remember how to factor from first semester?

• I don't remember factoring at all!

• I might remember some steps

• I feel confident in my ability to factor

Factoring Steps

 $3x^2+22x-16$  

Use an area model and diamond problem to factor quadratics

Step 1

Place your x² term and your constant diagonal from one another.

Multiple Choice

What do we do with those two values?

• Add them and put them in the bottom of the diamond

• Multiply them and put them in the bottom of the diamond

• Multiply them and put them in the top of the diamond

• Add them and put them in the top of the diamond

Step 2

Multiply your x² term and your constant. Place in the TOP of your diamond problem.

Open Ended

What goes in the bottom of your diamond problem?

$$3x^2+22x-16$$  

Step 3

Place your x term in the bottom of your diamond.

Step 4

Solve your diamond problem. Make a list of factors if it is helpful.

Multiple Choice

Which set of numbers should we use in our diamond problem?

• -1 & 48

• -2 & 24

• -3 & 16

• -4 & 12

• -6 & 8

Step 5

Place the values into the missing spaces in your area model.

Fill in the Blanks

Step 6 is to find the outside, and step 7 is to write your answer as a product. In the blank below, write your answer as a product. (use parenthesis, all lowercase letters, and no spaces)

Step 6 & 7

Find the outsides of your area model. Then write you answer as a product.

 $\left(3x-2\right)\left(x+8\right)$  



Multiple Choice

Factor completely: x²-6x+8

• (x-2)(x-4)
• (x-1)(x-8)
• (x+2)(x+4)
• (x+1)(x+8)

Multiple Choice

Factor completely:
 3x² + 5x - 12

• (3x + 4)(x-3)
• (3x - 4)(x + 3)
• (3x + 3)(x -4)
• (3x - 3)(x + 4)

When terms are missing

• use patterns like difference of squares

• factor out a gcf

• add a zero in for the missing term

Multiple Choice

Factor:x² - 25

• ( x + 5 ) ( x - 5 ) 
• ( x - 5 ) ( x - 5 ) 
• ( x + 5 ) ( x + 5 ) 
• Prime

Greatest Common Factor (GCF)

• When all factors of an expression share a common factor, we can factor it out

• Look at this expression:  $4x^2+10x-6$  

• Each term has a factor of 2

Greatest Common Factor (GCF)

• Each term has a 2 in it    $4x^2+10x-6$  

• Factor a 2 out     $2\left(2x^2+5x-3\right)$  

• Now use your box and diamond method to factor the terms in the parenthesis.

• At the end, make sure to include the 2 in your answer

•  $2\left(2x-1\right)\left(x+3\right)$  

Multiple Choice

Factor completely:
$$2x^2-6x-108$$  

• $$\left(x-9\right)\left(x+6\right)$$  

• $$2\left(x+9\right)\left(x-6\right)$$  

• $$2\left(x-9\right)\left(x+6\right)$$  

• $$\left(x+9\right)\left(x-6\right)$$