Factoring Trinomials using the box/area model

Factoring Trinomials using the box/area model

Review of GCF Factoring

• GCF factoring must always happen first for all other factoring to work properly

• Look for factors that appear in every single term to determine the GCF

• Factor the GCF out from every term. Put it in front of parentheses and put the remainder inside

Multiple Choice

 Factor completely:
 $16x^2-20xy$  
(Use your calculator to find the GCF)
Press MATH, Right Arrow ->, #9
gcd(16, 20)

•  $4xy\left(4x-5\right)$   
  

•  $4x^2\left(4-5y\right)$  
  

•  $4x\left(4x-5y\right)$  

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 c that add to b

• 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!

The Box Method/Area Model when a>1

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

• Multiply the a and the c

• Find the factors of ac that add to b

• 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!

Don't forget your signs!

The sign for the bottom row and right column always come from the first term in the row or column

Now you try some!

Multiple Choice

Find the expression that should replace D

• -5

• 5x

• -x

• -1

Multiple Choice

What expressions should replace C and E?

• C=2 and E=-1x

• C=2x and E=1x

• C=2x and E=-5x

• C=2x² and E=-5x

Fill in the Blanks

Factor completely
 $\ b^2+8b+7$  

do not use any spaces in your answer 

i.e. (p+r)(p-r) not ( p + r )(p -r) ect

Fill in the Blanks

Factor Completely
 $3p^2-2p-5$   

Do not use spaces in your answers

Fill in the Blanks

Factor completely $2k^2+22k+60$  

Don't forget to look for a GCF (if it has one it should in go in front of your factored answer)
and do not use spaces in your answer
i.e. GCF(p-r)(p+r)