Factoring trinomials recap

Draw a 2 x 2 table

Place one factor on the top of the table

Place the other factor on the left side of the table

Find the "area" of each cell by multiplying the edges.

Top left is x · x, this equals x²

Top right is a · x, this equals ax

Bottom left is b · x, this equals bx

Bottom right is a · b, this equals ab

Add all the 'areas'

Then you would combine like terms (ax + bx) = (a + b)x

Rewrite the trinomial

 $x^2\ +\ \left(a+b\right)x\ +\ ab$  

Since a & b are numbers, we can see the middle terms is the SUM of the consants and the last term is the PRODUCT of the same numbers

Let a = 2 and b = -3

Then we multiply (x + 2)(x - 3)

Set up Area Model

Find the area of each cell

Write out the SUM of the cells

Combine like terms

Final result is a trinomial

Remember, when we multiply, we place the 2 binomials outside on the top and left.

In factoring, we start with the first term inside top left.

Then place third term inside bottom right.

Let's factor x^2 + 3x + 2

What 2 number SUM to 3 and their PRODUCT is 2?

 $2\times1=2$  

 $2+1=3$  

Place these values inside the two remaining cells. (Order doesn't matter.)

Factor GCF out of top row

 $x^2+2x\rightarrow x\left(x+2\right)$  

Write X + 2 on the top of the model.

Factor GCF out of left column

 $x^2+x\rightarrow x\left(x+1\right)$  

Write X + 1 on the left side of the model.

SO, our factors for this trinomial are (x + 2)(x + 1 ) OR (x + 1)(x + 2)