Free Algebra
Tutorials!
 
Try the Free Math Solver or Scroll down to Tutorials!

 

 

 

 

 

 

 

 
 
 
 
 
 
 
 
 

 

 

 
 
 
 
 
 
 
 
 

Please use this form if you would like
to have this math solver on your website,
free of charge.


Factoring By Grouping

After studying this lesson, you will be able to:

  • Factor by grouping.

Steps of Factoring:

1. Factor out the GCF

2. Look at the number of terms:

  • 2 Terms: Look for the Difference of 2 Squares
  • 3 Terms: Factor the Trinomial
  • 4 Terms: Factor by Grouping

3. Factor Completely

4. Check by Multiplying

This lesson will concentrate on the second step of factoring: Factoring by Grouping.

**When there are 4 terms, we use factoring by grouping**

 

Example 1

Factor 3xy - 21y + 5x - 35

We have 4 terms, so we use factoring by grouping.

The first thing we do is the group the first 2 terms together and group the last 2 terms together. We do this by inserting parentheses.

( 3xy - 21y ) + ( 5x - 35 )

Now we work with the groups. We factor out the GCF in the first group and the GCF in the second group: 3y is the first GCF and +5 is the second GCF:

3y ( x - 7) +5 ( x -7 )

Now, we look at this as 2 terms... 3y ( x - 7 ) is the first term and 5 ( x - 7 ) is the second term.

We factor out what these 2 terms have in common - in this case they have x - 7 in common

So, we factor out x - 7 and we will have ( x - 7 ) ( 3y + 5 ) this is the answer

The 3y + 5 is what is left after we factored out x - 7

We can check the answer by multiplying ( x - 7 ) ( 3y + 5 ) use the FOIL method

3xy +5x -21y -35 this answer matches the original problem (order doesn't matter when adding)

 

Example 2

Factor 8m 2 n - 5m - 24mn + 15

We have 4 terms, so we use factoring by grouping.

The first thing we do is the group the first 2 terms together and group the last 2 terms together. We do this by inserting parentheses.

( 8m 2 n - 5 )( m - 24mn + 15 )

Now we work with the groups. We factor out the GCF in the first group and the GCF in the second group: m is the first GCF and -3 is the second GCF:

m ( 8mn - 5 ) (-3 ( 8mn - 5 ))

Now, we look at this as 2 terms... m ( 8mn - 5 ) is the first term and -3( 8mn - 5 ) is the second term.

We factor out what these 2 terms have in common -in this case they have 8mn - 5 in common

So, we factor out 8mn - 5 and we will have ( 8mn - 5 ) ( m - 3 ) this is the answer

The m - 3 is what is left after we factored out 8mn - 5

We can check the answer by multiplying ( 8mn - 5 ) ( m - 3 ) use the FOIL method

8m 2 n - 24mn - 5m + 15 this answer matches the original problem (order doesn't matter when adding)

 

Example 3

Factor 15x - 3xy + 4y - 20

We have 4 terms, so we use factoring by grouping.

The first thing we do is the group the first 2 terms together and group the last 2 terms together. We do this by inserting parentheses.

(15x - 3xy) (4y - 20)

Now we work with the groups. We factor out the GCF in the first group and the GCF in the second group: 3x is the first GCF and 4 is the second GCF:

3x ( 5 - y ) + 4 ( y - 5)

Notice that we don't have a common factor here. We have 5 - y and y - 5. They almost match but not quite. What we need to do is change the signs in the y - 5 and then we'll have a match. What we can do is to go back and factor out -4 instead of +4.

3x ( 5 - y ) -4 ( -y +5) [5 - y is the same as -y + 5]

We factor out what these 2 terms have in common - in this case they have 5 - y in common

So, we factor out 5 - y and we will have (5 - y) (3x - 4) this is the answer

We can check the answer by multiplying (5 - y) (3x - 4) use the FOIL method

15x - 20 - 3xy + 4y this answer matches the original problem (order doesn't matter when adding)

 
All Right Reserved. Copyright 2005-2018