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Warm up
Simplify
1. -5  x  4 
2.
3.
4.
 x  4  x  2 
 2 x  1 5 x  6 
2
 3x  2 
Answers
1.  5 x  20
2. x 2  2 x  8
3. 10 x 2  7 x  6
4. 9x  12 x  4
2
Factoring #1 GCF
Factoring is the opposite of
the distributive property.
We are going to undo
multiplication.
Let’s try it!
Let’s review
distributive
property
3( x  4)
3  x  (3  4)
3x 12
Look at the 2nd step. Do
you see the 3 in front of
the x and the -4?
3 is called the greatest
common factor for this
problem.
The first step in factoring is to
look for the GREATEST
COMMON FACTOR in all of the
terms.
The GCF is the largest number that divides into ALL terms evenly.
This is sometimes referred to as
the obvious term as well.
2x  6
2(
)
2(x + 3)
What is the Greatest Common
Factor between 2 and 6?
If you answered 2 you are correct!
Place that number OUTSIDE the ( )
Now divide both terms by 2 and place
the remainder in the ( ).
Let’s try another
one
3x  6 x  9
2
3(
)
Right! The 3 should remain
on the outside of the ( )
Now finish factoring.
3( x  2 x  3)
2
Think what is
the Greatest
number that can
be taken out of
each term?
If you answered 3 you
are correct do you
remember where it
should go in your
answer?
Let’s look at one more…
3a  6a  15a
4
3
2
What is the GCF for
this problem?
3a
2
Correct! Remember that the
GCF is in EVERY term and we
can include variables!
2
3a (
)
3a (a  2a  5)
2
2
Here are a few more
1) -40x8y6 – 16x9y5
2)
-2x3-6x2y
-8x8y5(5y + 2x)
-2x2(x + 3y)
Now you try!
1. 2 x  10
2(x – 5)
2. 30w  3w
2
3w(10w + 1)
3. 4x  12 x  18
2
4. 6 y  18 y  15 y
9
5
2(2x2 + 6x -9)
3
3y3(2y6-6y2 – 5)
Homework worksheet:
Factoring #1