Math Homework. Do It Faster, Learn It Better.

Factoring by Grouping

You can sometimes factor a difficult-looking polynomial by making creative use of the distributive property.

Example 1:

Factor 2xy6xz+3y9z .

You can get a clue from the coefficients: we have a 2 and a 6 , and we also have a 3 and a 9 . There is a proportional relationship here which can be exploited!

Factor 2x out of the first two terms:

2xy6xz+3y9z=2x( y3z )+3y9z

Then factor 3 out of the second two terms.

=2x( y3z )+3( y3z )

Since the same quantity y3z appears twice, we can use the distributive property to write this more simply:

=( 2x+3 )( y3z )

Example 2:

Factor x 2 +xy+3x+3y .

Group the terms as follows:

x 2 +xy+3x+3y=( x 2 +3x )+( xy+3y )

Both groups have x+3 as a factor.

=x( x+3 )+y( x+3 ) =( x+y )( x+3 )