Factor by Grouping
(or Split the Middle)
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This lesson will utilize Factoring by Grouping as an efficient method
of factoring a polynomial whose leading coefficient is NOT "1" .

 

Factor by Grouping   


To Factor the form  
1.  Find , called the Master Product.
2.  Find two factors of that add to
the center term
b (the coefficient of x).
3.  Write the center term using the sum of the 2 new factors, including the proper signs.
4.  Group the terms to form pairs - the first
two terms and the last two terms.  Factor each pair by finding common factors.
5.  Factor out the shared (common)
binomial parentheses. 

In step (3) the order of the center terms does not matter,
as the problem will factor properly either way.

 

Take a look at these two problems, where the signs might present a problem.


 


 

 
3.   
 
3. 

 

 

This process of factoring by grouping also works in simpler expressions,
where the leading coefficient is "1"

 

Factoring by Grouping condensed: 

1.  Find the product of
 ac.

2.  Find two factors of ac that add to up to b.

3.  Split the middle term into two terms using these factors.

4.  Group the four terms to form two pairs.

5.  Factor each pair.

6.  Factor out the common (shared) binomial parenthesis.

ax2 + bx + c